We show that local and semilocal strings in Abelian and non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex ...

We show that local and semilocal strings in Abelian and non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex ...

We use the moduli matrix approach to study the moduli space of 1/4 BPS kinks supported by vortices in the Higgs phase of N=2 supersymmetric U(N) gauge theories when non-zero masses for the matter hypermultiplets are introduced. We focus on the case of degenerate masses. In these special cases vortices acquire new orientational degrees ...

The main result of the paper is the statement that the 'smooth' measure of Masur and Veech is the unique measure of maximal entropy for the Teichm�ller flow on the moduli space of Abelian differentials. The proof is based on the symbolic representation of the flow in Veech's space of zippered rectangles. ...

We derive general expressions for the K�hler form of the L2-metric in terms of standard 2-forms on vortex moduli spaces. In the case of abelian vortices in gauged linear sigma-models, this allows us to compute explicitly the K�hler class of the L2-metric. As an application we compute the total volume of the ...

We calculate the Kaehler potential for the Samols metric on the moduli space of Abelian Higgs vortices on R{sub 2}, in two different ways. The first uses a scaling argument. The second depends on a variant of the relationship between accessory parameters and the regularized action in Liouville field theory. The Kaehler potential on the ...

We investigate vortices on a cylinder in supersymmetric non-Abelian gauge theory with hypermultiplets in the fundamental representation. We identify moduli space of periodic vortices and find that a pair of wall-like objects appears as the vortex moduli is varied. Usual domain walls also can be obtained from the ...

We study vortex dynamics in three-dimensional theories with Chern-Simons interactions. The dynamics is governed by motion on the moduli space M in the presence of a magnetic field. For Abelian vortices, the magnetic field is shown to be the Ricci form over M; for non-Abelian vortices, it is the first Chern ...

We study vortex dynamics in three-dimensional theories with Chern-Simons interactions. The dynamics is governed by motion on the moduli space M in the presence of a magnetic field. For Abelian vortices, the magnetic field is shown to be the Ricci form over M; for non-Abelian vortices, it is the first Chern ...

We completely determine the moduli space M{sub N,k} of k vortices in U(N) gauge theory with N Higgs fields in the fundamental representation. Its open subset for separated vortices is found as the symmetric product (CxCP{sup N-1}){sup k}/S{sub k}. Orbifold singularities of this space correspond to coincident vortices and are resolved ...

We give an overview of the work of Corlette, Donaldson, Hitchin and Simpson leading to the non-abelian Hodge theory correspondence between representations of the fundamental group of a surface (a surface group) and the moduli space of Higgs bundles. We then explain how this can be generalized to a correspondence between character ...

We describe the short-distance properties of the spacetime of a system of D particles by viewing their matrix-valued coordinates as coupling constants of a deformed world-sheet ? model. We show that the Zamolodchikov metric on the associated moduli space naturally encodes properties of the non-Abelian dynamics, and from this we derive ...

(0.1) We consider p-divisible groups (also called Barsotti-Tate groups) in characteristic p, abelian varieties, their deformations, and we draw some conclusions. For a p-divisible group (in characteristic p) we can define its Newton polygon. This is invariant under isogeny. For an abelian variety the Newton polygon of its p-divisible group is "symmetric". ...

A continuum of monopole, dyon, and black hole solutions exists in the Einstein-Yang-Mills theory in asymptotically anti-de Sitter space. Their structure is studied in detail. The solutions are classified by non-Abelian electric and magnetic charges and the Arnowitt-Deser-Misner mass. The stability of the solutions which have no node in ...

Magnetic monopoles in Yang-Mills-Higgs theory with a non-abelian unbroken gauge group are classified by holomorphic charges in addition to the topological charges familiar from the abelian case. As a result the moduli spaces of monopoles of given topological charge are stratified according to the holomorphic ...

The properties of BPS monopoles carrying nonabelian magnetic charges are investigated by following the behavior of the moduli space of solutions as the Higgs field is varied from a value giving a purely abelian symmetry breaking to one that leaves a nonabelian subgroup of the gauge symmetry unbroken. As the limit of nonabelian unbroken ...

We study three families of Atkin-Lehner quotients of quaternionic Shimura curves: X D+, X D+ 0 (N), and X D+ 1 (N), which serve as moduli spaces of abelian surfaces with potential quaternionic multiplication (PQM) and level N structure. The arithmetic geometry of these curves is similar to, but even richer than, that of the classical ...

The Bogomol'nyi-Prasad-Sommerfield (BPS) multiwall solutions are constructed in supersymmetric U(N{sub C}) gauge theories in five dimensions with N{sub F}(>N{sub C}) hypermultiplets in the fundamental representation. Exact solutions are obtained with full generic moduli for infinite gauge coupling and with partial moduli for finite gauge ...

We consider non-Abelian 1/2 Bogomol'nyi-Prasad-Sommerfield (BPS) flux tubes (strings) in a deformed N=2 supersymmetric gauge theory, with mass terms {mu}{sub 1,2} of the adjoint fields breaking N=2 down to N=1. The main feature of the non-Abelian strings is the occurrence of orientational moduli associated with the possibility ...

We review our recent works on solitons in U(NC) gauge theories with NF(? NC) Higgs fields in the fundamental representation, which possess eight supercharges. The moduli matrix is proposed as a crucial tool to exhaust all BPS solutions, and to characterize all possible moduli parameters. Since vacua are in the Higgs phase, we find domain walls (kinks) and ...

A string model for the short range interactions of vortices in the Goldstone and Abelian Higgs theory is presented. It is applied to the scattering of parallel vortices with a small impact parameter and reproduces the right-angle scattering accompanied by the occurrence of a superluminal velocity of the zeros of the Higgs field. The form of the metric on the vortex ...

Energy spectrum and degeneracy associated with bound states of monopoles and dyons in non-Abelian gauge theory has been investigated and it is shown that energy levels expand due to the presence of additional degeneracies. Splitting of energy level of dyonium in presence of external magnetic and electric field has also been analyzed confirming the presence of additional ...

After briefly reviewing the problems associated with non-Abelian monopoles, we turn our attention to the development in our understanding of non-Abelian vortices in the last several years. In the U(N) model with Nf = N flavors in which they were first found, the fluctuations of the orientational modes along the vortex length and in time become strongly ...

We address the problem of non-Abelian super-QCD, with a Fayet-Iliopoulos term, as seen from the vortex worldsheet perspective. Together with the FI term ?, also a mass ? for the adjoint superfield ? enters into the game. This mass allows the interpolation between {N} = 2 and {N} = 1 super-QCD. We distinguish, inside the parameter space spanned by ? ...

We address the problem of non-Abelian super-QCD, with a Fayet-Iliopoulos term, as seen from the vortex worldsheet perspective. Together with the FI term ?, also a mass � for the adjoint superfield ? enters into the game. This mass allows the interpolation between N = 2 and N = 1 super-QCD. We distinguish, inside the parameter space spanned by ? and ...

We find half-BPS vortex solitons, at both weak and strong coupling, in the Script N = 6 supersymmetric mass deformation of ABJM theory with U(N) � U(N) gauge symmetry and Chern-Simons level k. The strong coupling gravity dual is obtained by performing a Bbb Zk quotient of the Script N = 8 supersymmetric eleven dimensional supergravity background of Lin, Lunin and Maldacena corresponding to the ...

We study the energy density of two distinct fundamental monopoles in SU(3) and Sp(4) theories with an arbitrary mass ratio. Several special limits of the general result are checked and verified. Based on the analytic expression of energy density the coefficient of the internal part of the moduli space metric is computed, which gives it a nice ...

We present a class of supersymmetric models in which flavor symmetries are broken dynamically, by a set of composite flavon fields. The strong dynamics that is responsible for confinement in the flavor sector also drives flavor symmetry-breaking vacuum expectation values, as a consequence of a quantum-deformed moduli space. Yukawa couplings result as a ...

Ab Cats Alg Geom Moduli Derived Cats Triangulated Cats And Back Again Triangulated Categories in Algebraic Geometry Antony Maciocia May 21, 2010 #12;Ab Cats Alg Geom Moduli Derived Cats Triangulated Cats And Back Again Outline Abelian Categories #12;Ab Cats Alg Geom Moduli Derived Cats Triangulated Cats And Back

We study asymptotic relations connecting unipotent averages of {text{Sp}}left( {2g,mathbb{Z}} right) automorphic forms to their integrals over the moduli space of principally polarized abelian varieties. We obtain reformulations of the Riemann hypothesis as a class of problems concerning the computation of the equidistribution ...

In this note we study some aspects of the so-called dual ABJM theory introduced by Hanany, Vegh & Zaffaroni. We analyze the spectrum of chiral operators, and compare it with the spectrum of functions on the mesonic moduli space M = C^2 � C^2 Z_k , finding expected agreement for the coherent branch. A somewhat mysterious extra branch of dimension N 2 ...

We study the generic intersection (or web) of vortices with instantons inside, which is a 1/4 Bogomol�nyi-Prasad-Sommerfield state in the Higgs phase of five-dimensional N=1 supersymmetric U(NC) gauge theory on Rt�(C*)2?R2,1�T2 with NF=NC Higgs scalars in the fundamental representation. In the case of the Abelian-Higgs model (NF=NC=1), the intersecting vortex sheets can ...

We study generic intersection (or web) of vortices with instantons inside, which is a 1/4 BPS state in the Higgs phase of five-dimensional N=1 supersymmetric U(Nc) gauge theory on R_t \\times (C^\\ast)^2 \\simeq R^{2,1} \\times T^2 with Nf=Nc Higgs scalars in the fundamental representation. In the case of the Abelian-Higgs model (Nf=Nc=1), the intersecting vortex sheets can be ...

Vortices of a new type, carrying non-Abelian flux moduli CPn-1�CPr-1, are found in the context of softly broken N=2 supersymmetric quantum chromodynamics. By tuning the bare quark masses appropriately, we identify the vacuum in which the underlying SU(N) gauge group is partially broken to SU(n)�SU(r)�U(1)/ZK, where K is the least common multiple of ...

Effects of mass deformations on 1/2 Bogomol'nyi-Prasad-Sommerfield (BPS) non-Abelian vortices are studied in 4d N=2 supersymmetric U(1) \\times SO(2n) and U(1) \\times USp(2n) gauge theories, with Nf=2n quark multiplets. The 2d N=(2,2) effective worldsheet sigma models on the Hermitian symmetric spaces SO(2n)/U(n) and USp(2n)/U(n) found recently which ...

In this paper we outline some aspects of nonabelian gauged linear sigma models. First, we review how partial flag manifolds (generalizing Grassmannians) are described physically by nonabelian gauged linear sigma models, paying attention to realizations of tangent bundles and other aspects pertinent to (0, 2) models. Second, we review constructions of Calabi Yau complete intersections within such ...

The quantum worldsheet dynamics of vortex strings contains information about the 4d non-Abelian gauge theory in which the string lives. Here I tell this story. The string worldsheet theory is typically some variant of the CP sigma-model, describing the orientation of the string in a U(N) gauge group. Qualitative parallels between 2d sigma-models and 4d ...

Starting from Nahm{close_quote}s equations, we explore Bogomol{close_quote}nyi-Prasad-Sommerfield (BPS) magnetic monopoles in the Yang-Mills-Higgs theory of the gauge group Sp(4), which is broken to SU(2){times}U(1). There exists a family of BPS field configurations with a purely Abelian magnetic charge that describes two identical massive monopoles and one massless monopole. ...

We extend the stringy derivation of mathcal{N} = 2 AdS4/CFT3 dualities to cases where the M-theory circle degenerates at complex codimension-two submanifolds of a toric conical CY4. The type IIA backgrounds include D6-branes, and the dual mathcal{N} = 2 quiver gauge theories contain chiral flavors. We provide a general recipe to derive the geometric moduli ...

We review our recent work on solitons in the Higgs phase. We use U(NC) gauge theory with NF Higgs scalar fields in the fundamental representation, which can be extended to possess eight supercharges. We propose the moduli matrix as a fundamental tool to exhaust all BPS solutions, and to characterize all possible moduli parameters. ...

POISSON STRUCTURES ON MODULI SPACES OF REPRESENTATIONS WILLIAM CRAWLEY-BOEVEY Abstract. We show that a Poisson structure can be induced on the affine moduli space of (semisimple) representations algebras. We call such structures H0- Poisson structures, and show that they are well-behaved for Azumaya

We first study some explicit relations between the canonical line bundle and the Hodge bundle over moduli spaces for low genus. This leads to a natural measure on the moduli space of every genus which is related to the Siegel symplectic metric on Siegel u...

Two theorems in the mathematical theory of the Picard group of the moduli spaces of G-bundles are derived. 18 refs. (Atomindex citation 27:046055)

The purpose of the note is to announce canonical formulas for the higher-order tangent spaces to various moduli and deformation spaces. A basic case to which the results apply is that of the moduli of a compact complex manifold X, assumed for simplicity t...

We discuss statistics of vortices having zero-energy non-Abelian Majorana fermions inside them. Considering the system of multiple non-Abelian vortices, we derive a non-Abelian statistics that differs from the previously derived non-Abelian statistics. The non-Abelian statistics presented here ...

We discuss the quantum states in the moduli space, which are constructed with maximally charged dilaton black holes. Considering the quantum mechanics in the moduli space, we obtain the asymptotic states for the near-coincident black holes and the widely separated black holes. We study the scattering process of the ...

We study the generic intersection (or web) of vortices with instantons inside, which is a 1/4 Bogomol'nyi-Prasad-Sommerfield state in the Higgs phase of five-dimensional N=1 supersymmetric U(N{sub C}) gauge theory on R{sub t}x(C*){sup 2}{approx_equal}R{sup 2,1}xT{sup 2} with N{sub F}=N{sub C} Higgs scalars in the fundamental representation. In the case of the ...

In this note, we summarize recent progress in constructing and then semi-classically quantizing solitons, or non-abelian Q-balls, in the symmetric space sine-Gordon theories. We then consider the images of these solitons in the related constrained sigma model, which are the dyonic giant magnons on the string theory world-sheet. Focussing on the case of the ...

Poincar'e polynomial of the moduli spaces of parabolic bundles Yogish I. Holla March 7, 2000 School of the moduli spaces of semi�stable parabolic bundles on a curve. The quasi parabolic analogue of the Siegel for determine the Betti numbers of the moduli of semistable parabolic bundles on a ...

The BRST invariance of theories with local space-time symmetries, such as the reparametrization-invariant point-particle or d-dimensional general relativity, and of theories with local internal symmetries, like abelian and non-abelian gauge theories, can ...

The Abelian charges in a non-Abelian Yang-Mills-Dirac theory arising from the reduction of the structure group are studied. They are defined by the concept of the stabilizer gauge transformations. Their properties are investigated. The relationship between the whole class of stabilizer and the stratification of the space of gauge ...

We prove the formulae conjectured by the first author for the index of K-theory classes over the moduli stack of algebraic G-bundles on a smooth projective curve. The formulae generalise Verlinde's for line bundles and have Witten's integrals over the moduli space of stable bundles as their large level limits. As an application, we ...

A new compactification for the scheme of moduli for Gieseker-stable vector bundles with prescribed Hilbert polynomial on the smooth projective polarized surface (S,L) is constructed. We work over the field k=\\bar k of characteristic zero. Families of locally free sheaves on the surface S are completed with locally free sheaves on schemes which are modifications of S. The ...

We show that spherically-symmetric non-extremal black holes can be obtained as solutions to a set of BPS-like first-order equations. Because the Killing spinor equations for a supergravity theory are also first-order, this suggests that supersymmetry may play a hidden role in black hole solutions. We show that in the effective 1 + 1-dimensional action for the spherically-symmetric ansatz, the ...

We calculate the Luescher term for recently suggested non-Abelian flux tubes (strings). The main feature of the non-Abelian strings is the presence of orientational zero modes associated with rotation of their color flux inside a non-Abelian subgroup. The Luescher term is determined by the number of light degrees of freedom on the ...

The four-dimensional N=1 effective action of F-theory compactified on a Calabi�Yau fourfold is studied by lifting a three-dimensional M-theory compactification. The lift is performed by using T-duality realized via a Legendre transform on the level of the effective action, and the application of vector-scalar duality in three dimensions. The leading order K�hler potential and gauge-kinetic ...

We describe a set of methods to calculate gauge theory renormalization constants from string theory, all based on a consistent prescription to continue off shell open bosonic string amplitudes. We prove the consistency of our prescription by explicitly evaluating the renormalizations of the two, three and four-gluon amplitudes, and showing that they obey the appropriate Ward identities. The field ...

We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes ...

We study special points in the moduli space of vacua at which supersymmetric electric solutions of the heterotic string theory become massless. We concentrate on configurations for which the supersymmetric nonrenormalization theorem is valid. These are ten-dimensional supersymmetric string waves and generalized fundamental strings with SO(8) holonomy ...

The low energy spectrum of (3+1)-dimensional Script N = 4 supersymmetric Yang-Mills theory on a spatial three-torus contains a certain number of bound states, characterized by their discrete abelian magnetic and electric 't Hooft fluxes. At weak coupling, the wave-functions of these states are supported near points in the moduli space ...

Contents: Seminar on Singularities Moduli Questions Seminar on Etale Cohomology of Number Fields Elliptic Curves and Formal Groups Families of Abelian Varieties and Number Theory (Seminar on Hyperbolic Varieties and Informal Groups) Seminar on Commutative...

We show how to construct a topological quantum field theory which corresponds to a given moduli space. This method is applied to several cases. In particular we discuss the moduli space of flat gauge connections over a Riemann surface which is related to the phase space of the Chern-Simons ...

Conformally invariant (2+1)-dimensional gravity, Chern-Shimons gravity, is studied. Its solution space, moduli space, is investigated using the linearization method. The dimension of moduli space is determined as 18g - 18 for g > 1,6 for g = 1 and 0 for g...

the quilted Floer theory of Wehrheim and Woodward to families of quilted surfaces parametrized by the Stasheff- hedra are realized as a moduli space of quilted disks. Using the quilted disks we define the moduli space of pseudoholomorphic quilted disks, which under suitable transver- sality assumptions are smooth

We found double-extreme black holes associated with the special geometry of the Calabi-Yau moduli space with the prepotential F = STU. The area formula is STU-moduli independent and has (SL(2, Z))3 symmetry in space of charges. The dual version of this th...

In 1987, A. Floer suggested that Yang-Mills-Higgs theory should be studied on asymptotically Euclidean 3-manifolds M and it has been proved a rich subject in recent years. The focus of interest is the geometry of the moduli space of monopoles on M and its...

We consider N=2 supersymmetric QCD with the U(N) gauge group (with no Fayet-Iliopoulos term) and N{sub f} flavors of massive quarks deformed by the mass term {mu} for the adjoint matter, W={mu}A{sup 2}, assuming that N{<=}N{sub f}<2N. This deformation breaks N=2 supersymmetry down to N=1. This theory supports non-Abelian flux tubes (strings) which are stabilized ...

We consider N=2 supersymmetric QCD with the U(N) gauge group (with no Fayet-Iliopoulos term) and Nf flavors of massive quarks deformed by the mass term ? for the adjoint matter, W=?A2, assuming that N?Nf<2N. This deformation breaks N=2 supersymmetry down to N=1. This theory supports non-Abelian flux tubes (strings) which are stabilized by W. They are referred to as F-term ...

We investigate moduli stabilization in string gas compactification. We first present numerical evidence showing the stability of the radion and the dilaton. To understand this numerical result, we construct the 4-dimensional effective action by taking into account T-duality. It turns out that the dilaton is actually marginally stable. When the moduli other ...

We study two steps of moduli stabilization in type IIB flux compactification with gaugino condensations. We consider the condition that one can integrate out heavy moduli first with light moduli remaining. We give appendix, where detail study is carried out for potential minima of the model with a six dimensional compact ...

We provide an M theory interpretation of the recently discovered N=8 supersymmetric Chern-Simons theory with SO(4) gauge symmetry. The theory is argued to describe two membranes moving in the orbifold R8/Z2. At level k=1 and k=2, the classical moduli space M coincides with the infrared moduli space of SO(4) and ...

The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact K\\"{a}hler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact, K\\"{a}hler) structures $\\Omega_{\\Psi_0}$ on the moduli space, ...

to describe a few pysical theories in which moduli space plays an important role. However, I must say

The mechanism of non-Abelian color confinement is studied in SU(2) lattice gauge theory in terms of the Abelian fields and monopoles extracted from non-Abelian link variables without adopting gauge fixing. First, the static quark-antiquark potential and force are computed with the Abelian and monopole Polyakov loop ...

We find new non-Abelian flux tube solutions in a model of N{sub f} scalar fields in the fundamental representation of SU(N)xU(1) with N{<=}N{sub f} (the 'extended non-Abelian Higgs model'), and study their main properties. Among the solutions there are spinning strings as well as superconducting ones. The solutions exist only in a ...

The one dimensional quantum walk of anyonic systems is presented. The anyonic walker performs braiding operations with stationary anyons of the same type ordered canonically on the line of the walk. Abelian as well as non-Abelian anyons are studied and it is shown that they have very different properties. Abelian anyonic walks ...

The one dimensional quantum walk of anyonic systems is presented. The anyonic walker performs braiding operations with stationary anyons of the same type ordered canonically on the line of the walk. Abelian as well as non-Abelian anyons are studied and it is shown that they have very different properties. Abelian anyonic walks ...

The gauge theory with a topological N = 2 symmetry is discussed. This theory captures the de Rham complex and Riemannian geometry of some underlying moduli space M and the partition function equals the Euler number chi(M) of M. Moduli spaces of instantons...

Yang-Mills-Higgs theory in the Euclidean space R(sup 3) has been studied in various points of view for many years. A unifying theme of Yang-Mills-Higgs theory is the moduli space M(sup k) of charge k monopoles on M. It gives a cobordism of the moduli spac...

We study the natural compactification of the moduli space of branched minimal immersions of S(sup 2) into S(sup 4). We prove that the (compactified) moduli space M(sub d) is a connected projective variety of dimension 2d+4. It is irreducible when d=1,2, a...

For the description of extremal polynomials (that is, the typical solutions of least deviation problems) one uses real hyperelliptic curves. A partitioning of the moduli space of such curves into cells enumerated by trees is considered. As an application of these techniques the range of the period map of the universal cover of the ...

We classify parallelizable noncommutative manifold structures on finite sets of small size in the general formalism of framed quantum manifolds and vielbeins introduced previously [S. Majid, Commun. Math. Phys. 225, 131 (2002)]. The full moduli space is found for <=3 points, and a restricted moduli space for 4 ...

We study the moduli space of scalars in the BLG theory with and without a constant background four-form field. The classical vacuum moduli space is sixteen-dimensional in the absence of the four-form field. In its presence, however, the moduli space of BPS configurations ...

We perform a study of the moduli space of framed torsion-free sheaves on Hirzebruch surfaces by using localization techniques. We discuss some general properties of this moduli space by studying it in the framework of Huybrechts-Lehn theory of framed modules. We classify the fixed points under a toric action on the ...

Jun 15, 2011 ... Abelian groups; algebraic systems; Banach spaces; Boolean algebra; differential geometry; field theory (mathematics); fractals ...

This article is a survey of results on the arithmetic of Abelian varieties that have been obtained by cohomological methods. It consists of an Introduction and six sections. In the Introduction the main facts to be proved in the article are stated. They are concentrated around two arithmetical problems: the determination of the rank of an Abelian variety ...

Gauge theories on q-deformed spaces are constructed using covariant derivatives. For this purpose a ''vielbein'' is introduced, which transforms under gauge transformations. The non-Abelian case is treated by establishing a connection to gauge theories on commutative spaces, i.e. by a Seiberg-Witten ...

We study quantum effects on moduli dynamics arising from the production of particles which are light at points of enhanced symmetry in moduli space. The resulting forces trap the moduli at these points. Moduli trapping occurs in time-dependent quantum field theory, as well as in systems of ...

We present ADHM-Nahm data for instantons on the Taub-NUT space and encode these data in terms of Bow Diagrams. We study the moduli spaces of the instantons and present these spaces as finite hyperk�hler quotients. As an example, we find an explicit expression for the metric on the moduli ...

While the number of metastable landscape vacua in string theory is vast, the number of supermoduli vacua which lead to distinct low-energy physics is even larger, perhaps infinitely so. From the anthropic perspective it is therefore important to understand whether complex life is possible on moduli space - i.e., in low-energy effective theories with (1) ...

While the number of landscape vacua in string theory is vast, the number of supermoduli vacua which lead to distinct low energy physics is even larger, perhaps infinitely so. From the anthropic perspective it is therefore important to understand whether complex life is possible on moduli space -- i.e., in low energy effective theories with 1. exact ...

Non-Abelian vortices are topologically stable objects in the color-flavor locked phase of dense QCD. We derive a dual Lagrangian starting with the Ginzburg-Landau effective Lagrangian for the color-flavor locked phase, and obtain topological interactions of non-Abelian vortices with quasiparticles such as U(1)B Nambu-Goldstone bosons (phonons) and massive ...

Recently, Foulis (Foulis, D. J. (2003). Compressible groups, Mathematica Slovaca 53, 433 455.) characterized compressions on effect rings, which were introduced as a generalization of unital C*-algebras in the context of ordered abelian groups with order units. In the present paper, we characterize a class of symmetries on effect rings and show their relations to compressions. ...

We consider the minimal model in which dark matter is stabilized by a non-Abelian discrete symmetry. The symmetry group is taken to be D?S, which is the smallest non-Abelian finite group. The minimal model contains (nontrivial) singlet and doublet scalar representations of D which couple to the Standard Model fields via the Higgs portal. This construction ...

We describe how the entanglement renormalisation approach to topological lattice systems leads to a general procedure for treating the whole spectrum of these models in which the Hamiltonian is gradually simplified along a parallel simplification of the connectivity of the lattice. We consider the case of Kitaev's quantum double models, both Abelian and ...

Using path-integral methods and /zeta/-function regularization a nonperturbative derivation of non-Abelian-covariant and consistent anomalies on a curved space with torsion is given. All terms depending on torsion, that one has in the expression of the consistent anomaly, can be eliminated by adding suitable counterterms to the Lagrangian density. In this ...

An Abelian gauge symmetry can be spontaneously broken near a black hole horizon in anti-de Sitter space using a condensate of non-Abelian gauge fields. A second order phase transition is shown to separate Reissner-Nordstr�m-anti-de Sitter solutions from a family of symmetry-breaking solutions which preserve a diagonal combination of ...

An Abelian gauge symmetry can be spontaneously broken near a black hole horizon in anti-de Sitter space using a condensate of non-Abelian gauge fields. A second order phase transition is shown to separate Reissner-Nordstroem-anti-de Sitter solutions from a family of symmetry-breaking solutions which preserve a diagonal combination of ...

An Abelian gauge symmetry can be spontaneously broken near a black hole horizon in anti de Sitter space using a condensate of non-Abelian gauge fields. A second order phase transition is shown to separate Reissner Nordstr�m anti de Sitter solutions from a family of symmetry-breaking solutions which preserve a diagonal combination of ...

In this paper the amplitudes of bosonic string theory on Riemann surfaces are studied taking the branch points as moduli. The case of a general Riemann surface of genus three is completely worked out, constructing the chiral determinants and the propagators. The chiral determinants and the partition function are given explicitly in terms of the moduli and ...

This thesis investigates the metric dependence of the moduli spaces of Yang-Mills fields of an SU(2) principal bundle P with chern number -1 over a four-dimensional, simply-connected, oriented, compact smooth manifold M with positive definite intersection form. The purpose of this investigation is to suggest that the surgery class of the ...

We describe a simple class of type IIA string compactifications on Calabi-Yau manifolds where background fluxes generate a potential for the complex structure moduli, the dilaton, and the Kaehler moduli. This class of models corresponds to gauged {Nu} = 2 supergravities, and the potential is completely determined by a choice of gauging and by data of the ...

Starting from a recently proposed Abelian topological model in 2+1 dimensions, which involve the Kalb-Ramond two form field, we study a non-Abelian generalization of the model. An obstruction for the generalization is detected. However, we show that the goal is achieved if we introduce a vectorial auxiliary field. Consequently, a model is proposed, ...

We deduce a new set of symmetries and relations between the coefficients of the expansion of Abelian and non-Abelian fractional quantum Hall (FQH) states in free (bosonic or fermionic) many-body states. Our rules allow us to build an approximation of a FQH model state with an overlap increasing with growing system size (that may sometimes reach unity) ...

We deduce a new set of symmetries and relations between the coefficients of the expansion of Abelian and non-Abelian fractional quantum Hall (FQH) states in free (bosonic or fermionic) many-body states. Our rules allow us to build an approximation of a FQH model state with an overlap increasing with growing system size (that may sometimes reach unity) ...

We propose a generalized quantum geometric tenor to understand topological quantum phase transitions, which can be defined on the parameter space with the adiabatic evolution of a quantum many-body system. The generalized quantum geometric tenor contains two different local measurements, the non-Abelian Riemannian metric and the ...

The primary topic of this work is the solution of string theories compactified on a Calabi-Yau manifold. The prepotentials and the geometry of the moduli spaces for a Calabi-Yau manifold and its mirror are computed. In this way all sigma model corrections to the Yukawa couplings and moduli space metric for the ...

We present a supersymmetric extension of the standard model (USSM-A) with an anomalous U(1) and Stueckelberg axions for anomaly cancellation, generalizing similar nonsupersymmetric constructions. The model, built by a bottom-up approach, is expected to capture the low-energy supersymmetric description of axionic symmetries in theories with gauged anomalous Abelian ...

In the first part of this thesis we study effective action of the theories with gauge symmetry spontaneously broken by the Higgs mechanism. The effective action of such Higgs theories should be gauge-invariant. However, the quantum and/or thermal contributions to the effective potential seem to be gauge-dependent, posing a problem for its physical interpretation. We identify the source of the ...

We extend previous work on non-abelian T-duality in the presence of Ramond fluxes to cases in which the duality group acts with isotropy such as in backgrounds containing coset spaces. In the process we generate new supergravity solutions related to D-brane configurations and to standard supergravity compactifications.

The periodic non-Abelian space-independent solutions to Yang--Mills SU(2) equations are studied. Hopf bifurcation is shown to appear. New analytic solutions generating a simple Abelian source are found and their stability is discussed. The source can be produced by a fermion field; a self-consistent solution of Yang--Mills--Dirac ...

Abelian gauge theories are quantized in a geometric representation that generalizes the loop representation and treats electric and magnetic operators on the same footing. The usual canonical algebra is turned into a topological algebra of nonlocal operators that resembles the order-disorder dual algebra of �t Hooft. These dual operators provide a complete description of the ...

Superposed electrovac pp-waves causes chaos. To show this, we project the particle geodesics onto the (x,y) plane and simulate the phase space's Poincare section numerically. Similar considerations apply, with minor modifications, to the geodesics in a non-Abelian plane wave spacetime.

We quantize the (1+1)-dimensional Abelian gauge theory on cylinder to illustrate our idea how to extract global modes of topological orign. A new analysis is made for the (2+1)-dimensional Maxwell theory on T/sup 2/(torus) x R(time). The dynamics is expli...

candidate for a cohomology theory AG which gives rise to the formal group G. Namely, for every finite cell spaces (Y X) to abelian groups. (We recover the absolute cohomology groups An (X) by taking Y = .) (2 of cohomology with coefficients in any abelian group M: one simply replaces Z by M in the statement

This is a survey of our recent results on the geometry of moduli spaces and Teichmuller spaces of Riemann surfaces appeared in math.DG/0403068 and math.DG/0409220. We introduce new metrics on the moduli and the Teichmuller spaces of Riemann surfaces with very good properties, study their ...

In this paper, an approach to instantons in supersymmetrical 2-dimensional sigma models is discussed. In this approach superinstantons are characterized as the superconformal maps of a physical space into the isotopic (target) space. The authors consider a special case of the supersphere with punctures. New topological invariants as the number of the ...

We show that a system of parallel D3 branes near a conifold singularity can be mapped onto an intersecting configuration of orthogonal branes in type IIA string theory. Using this brane configuration, we analyze the Higgs moduli space of the associated field theory. The dimension of the Higgs moduli space is ...

We give an a priori construction of the two-dimensional reduction of three-dimensional quantum Chern-Simons theory. This reduction is a two-dimensional topological quantum field theory and so determines to a Frobenius ring, which here is the twisted equivariant K-theory of a compact Lie group. We construct the theory via correspondence diagrams of moduli ...

Let G be locally compact abelian group and GAMMA its dual group. Let X be locally convex complete space and X* its dual space. In this paper we give spectral characterization of bounded uniformly continuous functions from G to X. Also, we give application...

In N=2 ungauged supergravity we have found the most general double-extreme dyonic black holes with arbitrary number n{sub v} of constant vector multiplets and n{sub h} of constant hypermultiplets. They are double-extreme: (1) supersymmetric with coinciding horizons, (2) the mass for a given set of quantized charges is extremal. The spacetime is of the Reissner-Nordstroem form and the vector ...

The modular measure corresponding to the contribution to the string partition function from the surface with {ital n} handles and {ital m}+1 holes is calculated.

... work on the moduli spaces of self dual Yang-Mills-Higgs connections on the compliment of a knot in R' and a study of the Skyrme model using the ...

Recently, an exact description of instanton corrections to the moduli spaces of 4d N = 2 supersymmetric gauge theories compactified on a circle and Calabi-Yau compactifications of Type II superstring theories was found. The equations determining the instanton contributions turn out to have the form of Thermodynamic Bethe Ansatz. We explore further this ...

The pore space compressibility of a rock provides a robust, model-independent descriptor of porosity and pore fluid effects on effective moduli. The pore space compressibility is also the direct physical link between the dry and fluid-saturated moduli, and is therefore the basis of Gassmann`s equation for fluid ...

Most modern approaches to Grand Unification incorporate alongside gravity very weak scalar fields or moduli that couple to matter in Equivalence-violating ...

Let Y be a smooth Calabi�Yau hypersurface of P1�P where P stands for a Pd-bundle over P1. We will prove that for many ample line bundles L and certain Chern characters c, the moduli space M(c) (resp.ML(c)) of L-Gieseker semistable (resp. L-stable ) rank two torsion free sheaves (resp. vector bundles) on Y with Chern character c are smooth and ...

Dependence of the gauge couplings on the moduli of the compactified space is studied for orbifold compactifications of the heterotic superstring. It is shown that such dependence is possible only for theories with sectors preserving N = 2 spacetime supers...

... In particular, we have explained which A-branes on the Hitchin moduli space correspond to the B-branes supported at orbifold singu- lar points of ...

the Fano threefold V5. Communications in Algebra 33, No. 9, 3061-3080 (2005). 15. Moduli space of a family

This work extends to the /D-dimensional space-time the topological mass generation mechanism of the non-abelian BF model in four dimensions. In order to construct the gauge invariant non-abelian kinetic terms for a (/D-2)-form /B and a 1-form /A, we introduce an auxiliary (/D-3)-form /V. Furthermore, we obtain a complete set of BRST ...

We describe hierarchies of exact string backgrounds obtained as non-Abelian cosets of orthogonal groups and having a space-time realization in terms of gauged WZW models. For each member in these hierarchies, the target-space backgrounds are identified with the ``boundary'' backgrounds of the next member. We explicitly demonstrate that ...

The theory of super Riemann surfaces is rigorously developed using Rogers' theory of supermanifolds. The global structures of super Teichmueller space and super moduli space are determined. The super modular group is shown to be precisely the ordinary modular group. Super moduli space ...

We present the coset structure of the untwisted moduli space of heterotic (0,2) Z(sub N) orbifold compactifications with continuous Wilson lines. For the cases where the internal 6-torus T(sub 6) is given by the direct sum T(sub 4) + T2, we explicitly con...

One loop scalar masses induced by Fayet-Ilipoulos D terms in string theory are calculated directly in the heterotic string theory for an arbitrary compactification which preserves space-time supersymmetry at the string tree level. The result is shown to be a total derivative in the moduli space of a torus with two punctures, and hence ...

We propose a scenario to stabilize all geometric moduli�that is, the complex structure, K�hler moduli, and the dilaton�in smooth heterotic Calabi-Yau compactifications without Neveu-Schwarz three-form flux. This is accomplished using the gauge bundle required in any heterotic compactification, whose perturbative effects on the ...

We study (3+1)-dimensional Script N = 4 supersymmetric Yang-Mills theory on a spatial three-torus. The low energy spectrum consists of a number of continua of states of arbitrarily low energies. Although the theory has no mass-gap, it appears that the dimensions and discrete abelian magnetic and electric 't Hooft fluxes of the continua are computable in a semi-classical ...

We study magnetic flux tubes in the Higgs vacuum of the {N} = 1* mass deformation of SU(Nc), {N} = 4 { {SYM}} and its large Nc string dual, the Polchinski-Strassler geometry. Choosing equal masses for the three adjoint chiral multiplets, for all Nc we identify a "colour-flavour locked" symmetry, SO(3)C+F which leaves the Higgs vacuum invariant. At weak coupling, we find explicit ...

We study magnetic flux tubes in the Higgs vacuum of the N = 1* mass deformation of SU(Nc), N = 4 SYM and its large Nc string dual, the Polchinski-Strassler geometry. Choosing equal masses for the three adjoint chiral multiplets, for all Nc we identify a "colour-flavour locked" symmetry, SO(3)C+F which leaves the Higgs vacuum invariant. At weak coupling, we find explicit ...

Within a class of superstring vacua which have an additional nonanomalous U(1){sup {prime}} gauge factor, we address the scale of the U(1){sup {prime}} symmetry breaking and constraints on the exotic particle content and their masses. We also show that an extra gauge U(1){sup {prime}} provides a new mechanism for generating a naturally small effective {mu} term. In general, existing models are not ...

A method to repair - ''blow-up'' - the singularities of the Abelian (2,2) orbifolds to obtain the corresponding (2,2) Calabi-Yau manifolds is presented. This approach makes use of the fact that with each orbifold singularity there are associated massless scalar fields - blowing-up modes - whose potential is flat to all orders in the string ...

Let E be a homotopy commutative ring spectrum, and suppose the ring of cooperations E#E is flat over E# . We wish to address the following question: given a commutative E# -algebra A in E#E-comodules, is there an E# -ring spectrum X with E#X = A as comodule algebras? We will formulate this as a moduli problem, and give a way -- suggested by work of Dwyer, Kan, and ...

For moduli space of stable parabolic bundles on a compact Riemann surface, we derive an explicit formula for the curvature of its canonical line bundle with respect to Quillen�s metric and interprete it as a local index theorem for the family of �?-operators in the associated parabolic endomorphism bundles. The formula consists of two terms: one ...

We analyze the link between the occurrence of massless B-type D-branes for specific values of moduli and monodromy around such points in the moduli space. This allows us to propose a classification of all massless B-type D-branes at any point in the moduli space of Calabi Yau�s. This ...

In the pure Einstein-Yang-Mills theory in four dimensions there exist monopole and dyon solutions. The spectrum of the solutions is discrete in asymptotically flat or de Sitter space, whereas it is continuous in asymptotically anti-de Sitter space. The solutions are regular everywhere and specified with their mass, and non-Abelian ...

It has been known for some time that for a large class of nonlinear field theories in Minkowski space with two-dimensional target space the complex eikonal equation defines integrable submodels with infinitely many conservation laws. These conservation laws are related to the area-preserving diffeomorphisms on target space. Here we ...

We study an extension of the procedure to construct duality transformations among abelian gauge theories to the non abelian case.

We examine the star lattice Kitaev model whose ground state is a chiral spin liquid. We fermionize the model such that the fermionic vacua are toric-code states on an effective Kagome lattice. This implies that the Abelian phase of the system is inherited from the fermionic vacua and that time-reversal symmetry is spontaneously broken at the level of the vacuum. In terms of ...

We show that a minimal clone has a nontrivial weakly abelian representation iff it has a nontrivial abelian representation, and that in this case all representations are weakly abelian.

We have analyzed, calculated and extended the modification of Maxwell's equations in a complex Minkowski metric, M4 in a C2 space using the SU2 gauge, SL(2,c) and other gauge groups, such as SUn for n>2 expanding the U1 gauge theories of Weyl. This work yields additional predictions beyond the electroweak unification scheme. Some of these are: 1) modified gauge invariant ...

Inflationary potentials are investigated for specific models in type IIB string theory via flux compactification. As concrete models, we investigate several cases where the internal spaces are weighted projective spaces. The models we consider have two, three, or four K�hler moduli. The K�hler moduli play a ...

We construct five new quantum Newton-Hooke Hopf algebras with the use of Abelian twist procedure. Further we demonstrate that the corresponding deformed spacetimes with quantum space and classical time are periodic or expanding in time.

By using a grassmanian polymer representation for the Fermionic functional determinant we argue the triviality of the vectorial four fermion interaction for space-time with dimensionality greater than two. (author). (Atomindex citation 22:067265)

Use of the surrogate zeta-function method was crucial in calculating the Casimir energy in non-Abelian Kaluza-Klein theories. We establish the validity of this method for the case that the background metric is (Euclidean space)x(N-sphere). Our techniques ...

... on a pseudo-metric un- bounded space (T, p) equipped with an abelian group-operation + such ... N SU {( 7 ()-( 7 i))>Pn/U, W(t1(s) >U, 0(71 ..1(S)) u ...

The non-Abelian magnetic monopoles associated with symmetry breaking by the compactification of extra dimensions is considered. It is shown that the spherically symmetric monopoles which satisfy the twisted boundary condition on the space cannot exist. (E...

It is shown that the Lorentz invariance is broken in gauge theories of chiral Weyl fermions in flat space-time via one-loop quantum corrections. Abelian gauge fields contribute to this anomaly in even dimensions larger than or equal to four and non-Abelia...

We show that the duality transformation in statistical mechanics which connects high and low temperature regime is the usual x-operation in differential geometry (a simple example of which is the correspondence between equipotentials and streamlines). We ...

We present the current algebra of a particular form in the nonlinear ?-model. The algebra has a non-Abelian form with field-dependent structure functions. We comment on the connection of the model with noncommutative space.

Local and global properties of the moduli space of Calabi--Yau type compactifications determine the low energy parameters of the string effective action. We show that the moduli space geometry is entirely encoded in the Picard--Fuchs equations for the periods of the Calabi--Yau [ital H][sup (3)]-cohomology. ...

We compute the period integrals on degenerate Seiberg�Witten curves for supersymmetric QCD explicitly and also show how these periods determine the changes in the quantum numbers of the states when passing from the weak- to strong-coupling domains in the mass moduli space of the theory. We discuss the confinement of monopoles at a strong coupling and ...

We discuss the moduli space of nine dimensional N = 1 supersymmetric compactifications of M theory/string theory with reduced rank (rank 10 or rank 2), exhibiting how all the different theories (including M theory compactified on a Klein bottle and on a M...

= 2 this is just the Teichmueller space and for N > 2 it is homeomorphic to an open ball of dimension the surface. In an article with Hugo Parlier [16] we study the following three questions: Is there a surface. A picture of moduli space. Invent. Math., 126(2):341�390, 1996. [16] Greg McShane and Hugo Parlier

#'s multiplihedron geometrically as the moduli space of stable quilted disks. This generalizes the geometric#. We consider a moduli space M n,1 of marked quilted disks, which are disks with n + 1 marked points z�marked quilted disk M n,1 is isomorphic as a CW�complex to the multiplihedron J n . Another ...

], [HM2]. There is some recent work of Gabi Farkas extending the work of Eisenbud, Harris, Mumford divisors on Mg? See [HMo], [GKM], [FaP3]. Deepee Khosla and Gabi Farkas have some fascinating new work surfaces. See for example, [BT], [HT], [Br]. It would be fun to explore recent work of Ronald van Luijk

Motivated by the heavy ion collision experiments there is much activity in studying the hydrodynamical properties of non-Abelian (quark-gluon) plasmas. A major question is how to deal with color currents. Although not widely appreciated, quite similar issues arise in condensed matter physics in the context of the transport of spins in the presence of spin-orbit coupling. The ...

Motivated by the heavy ion collision experiments there is much activity in studying the hydrodynamical properties of non-Abelian (quark gluon) plasmas. A major question is how to deal with color currents. Although not widely appreciated, quite similar issues arise in condensed matter physics in the context of the transport of spins in the presence of spin orbit coupling. The ...

A continuum of new monopole and dyon solutions in the Einstein-Yang-Mills theory in asymptotically anti-de Sitter space are found. They are regular everywhere and specified by their mass and their non-Abelian electric and magnetic charges. A class of monopole solutions which have no node in non-Abelian magnetic fields is shown to be ...

A field theory on a (d+n)-dimensional manifold in the presence of an n-dimensional isometry group spanning n-dimensional orbit spaces may be reduced to a field theory on a d-dimensional manifold. The field content of such reduced theories is completely worked out when the isometries may be non-Abelian and the resultant space may have ...

A duality transformation of a non abelian Thirring model with coupling constant ? and level k to one with coupling 1/? and level (-k-2Q) is derived. At ?=1 the theory acquires two dimensional gauge invariance, which freezes the current degrees of freedom. This point is infinitely far away from the origin in field space. It serves as a boundary between ...

We generalize the concept of Sato Grassmannians of locally linearly compact topological vector spaces (Tate spaces) to the category limA of the "locally compact objects" of an exact category A, and study some of their properties. This allows us to generalize the Kapranov dimensional torsor Dim(X) and determinantal gerbe Det(X) for the objects of limA and ...

We address the properties of self-gravitating domain walls arising from the breaking of an SU(N)�Z2-symmetric theory. In the particular case of N=5, we find that the two classes of stable non-Abelian kinks possible in flat space, that break SU(5) to its maximal subgroups, have an analogue in the gravitational case, and construct the analytical solutions. ...

We study the phase structure of a three-dimensional (3D) Abelian Higgs model with singly and doubly charged scalar fields coupled to a compact Abelian gauge field. The model is pretending to describe systems of strongly correlated electrons such as high-T{sub c} superconductivity in overdoped regime and exotic phases supporting excitations with ...

We investigate the transmutation of D-branes into Abelian magnetic backgrounds on the world-volume of higher-dimensional branes, within the framework of global models with compact internal dimensions. The phenomenon, T-dual to brane recombination in the intersecting-brane picture, shares some similarities to inverse small-instanton transitions in non-compact ...

The most fundamental strings in high-density color superconductivity are the non-Abelian semisuperfluid strings which have color-gauge flux tubes but behave as superfluid vortices in the energetic point of view. We show that in addition to the usual translational zero modes, these vortices have normalizable orientational zero modes in the internal space, ...

We investigate particle production near extra species loci (ESL) in a higher dimensional field space and derive a speed limit in moduli space at weak coupling. This terminal velocity is set by the characteristic ESL-separation and the coupling of the extra degrees of freedom to the moduli, but it is independent of ...

A braneworld model for neutrino dark energy (DE) is presented. We consider a five-dimensional two-branes setup with a bulk scalar field motivated by supergravity. Its low-energy effective theory is derived with a moduli space approximation. The position of the two branes are parametrized by two scalar degrees of freedom (moduli). After ...

Yang-Mills instantons on ALE gravitational instantons were constructed by Kronheimer and Nakajima in terms of matrices satisfying algebraic equations. These were conveniently organized into a quiver. We construct generic Yang-Mills instantons on ALF gravitational instantons. Our data are formulated in terms of matrix-valued functions of a single variable, that are in turn organized into a bow. We ...

We explore the possibility that quantum cosmology considerations could provide a selection principle in the landscape of string vacua. We propose that the universe emerged from the string era in a thermally excited state and determine, within a mini-superspace model, the probability of tunneling to different points on the landscape. We find that the potential energy of the tunneling endpoint from ...

We explore the possibility that quantum cosmology considerations could provide a selection principle in the landscape of string vacua. We propose that the universe emerged from the string era in a thermally excited state and determine, within a mini-superspace model, the probability of tunneling to different points on the landscape. We find that the potential energy of the tunneling endpoint from ...

Using ab initio calculations we have computed the lattice constants, bulk moduli, and local and total density of states of the MAX phases, Ti2TlC, Zr2TlC, and Hf2TlC in the hexagonal P63/mmc space group. The results for lattice constants are within 2% of experimental results. The bulk moduli are predicted to be 125, 120, and 131 GPa, ...

The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of twisted self-duality equations. These first-order equations relate the p-form fields to their dual forms by demanding that their respective field strengths are dual to each other. It is well known that such equations can be integrated to a local action that carries on equal ...

A Riemannian metric on a compact four-manifold induces a natural L^2 metric on the corresponding moduli space of (anti-) self-dual connections on a principal G-bundle P. When the bundle structure group G is SU(2) and -c_2(P) = k, Groisser, Parker and others have found explicit formulas for the components of the L^2 metric on the moduli ...

The theory of super Riemann surfaces is rigorously developed using Rogers' theory of supermanifolds. The global structures of super Teichmueller space and super moduli space are determined. The super modular group is shown to be precisely the ordinary mod...

The symmetries associated with the bosonic string partition function integral are examined so that the integration region in Teichmuller space can be determined. The translation of the conditions on the period matrix defining the fundamental region can be...

We obtain the behavior of the Wilson loop, under certain approximations, in the fermion--non-Abelian-vortex system defined in (2+1)-dimensional space-time. Our procedure consists of the restriction to the J = 0 channel for the quantum fluctuation around the vortex sector and s component for the fermionic wave function. We analyze the Wilson loops for the ...

We study at the classical and quantum mechanical level the time-dependent Yang-Mills theory that one obtains via the generalisation of discrete light-cone quantization to singular homogeneous plane waves. The non-Abelian nature of this theory is known to be important for physics near the singularity, at least as far as the number of degrees of freedom is concerned. We will ...

We study the properties of an ultracold Fermi gas loaded in an optical square lattice and subjected to an external and classical non-Abelian gauge field. We show that this system can be exploited as an optical analogue of relativistic quantum electrodynamics, offering a remarkable route to access the exotic properties of massless Dirac fermions with cold atoms experiments. In ...

We explore the low-temperature behavior of the Abelian Higgs model in AdS4, away from the probe limit in which back-reaction of matter fields on the metric can be neglected. Over a significant range of charges for the complex scalar, we observe a second order phase transition at finite temperature. The symmetry-breaking states are superconducting black holes. At least when the ...

Chiral partition functions of conformal field theory describe the edge excitations of isolated Hall droplets. They are characterized by an index specifying the quasiparticle sector and transform among themselves by a finite-dimensional representation of the modular group. The partition functions are derived and used to describe electron transitions leading to Coulomb blockade conductance peaks. We ...

The author reviews basic forces on moduli that lead to their stabilization, for example in the supercritical and KKLT models of de Sitter space in string theory, as well as an AdS(sub 4) x S(sup 3) x S(sup 3) model the author includes which is not publish...

We consider a compactification with a six-dimensional torus in the type II brane gas models. We show that the dilaton and the scale of each cycle of the internal space are fixed in the presence of NS5-branes and Kaluza-Klein monopoles as well as D-branes with the gauge fields. We can construct various models that lead to fixed moduli by using T-duality ...

We study the hypermultiplet moduli space of an N=4, U(Q(sub 1)) x U(Q(sub 5) ) gauge theory in 1 + 1 dimensions to extract the effective SCFT description of near extremal 5-dimensional black holes modelled by a collection D1- and D5- branes. On the moduli...

We construct extremal, spherically symmetric black hole solutions to 4D supergravity with charge assignments that preclude BPS-saturation. In particular, we determine the ground state energy as a function of charges and moduli. We find that the mass of the non-BPS black hole remains that of a marginal bound state of four basic constituents throughout the entire ...

In supersymmetric theories, the presence of axions usually implies the existence of a noncompact, (pseudo)moduli space. In gauge-mediated models, the axion would seem a particularly promising dark matter candidate. The cosmology of the moduli then constrains the gravitino mass and the axion decay constant; the former cannot be much ...

We compute the one-loop gauge couplings in six-dimensional non-Abelian gauge theories on the T{sup 2}/Z{sub 2} orbifold with general GUT breaking boundary conditions. For concreteness, we apply the obtained general formulas to the gauge coupling running in a 6D SO(10) orbifold GUT where the GUT group is broken down to the standard model gauge group up to an extra U(1). We find ...

In this paper we study the relationship between two different compactifications of the space of vector bundle quotients of an arbitrary vector bundle on a curve. One is Grothendieck's Quot scheme, while the other is a moduli space of stable maps to the relative Grassmannian. We establish an essentially optimal upper bound on the ...

We show how to implement T-duality along non-abelian isometries in backgrounds with non-vanishing Ramond fields. When the dimension of the isometry group is odd (even) the duality swaps (preserves) the chirality of the theory. In certain cases a non-abelian duality can result in a massive type-IIA background. We provide two examples by dualising SU(2) ...

We demonstrate the existence of a new topologically ordered phase in Kitaev's honeycomb lattice model. This new phase appears due to the presence of a tightly packed vortex lattice and it supports chiral Abelian anyons. We characterize the phase by its low-energy behavior that is described by four Fermi points as opposed to two Fermi points in the absence of the vortex ...

The formation of monopoles and their condensation in the QCD ground state is a feature which is related to abelian gauge fixing, discussed in this chapter. The gluon field acquires a singularity in the vicinity of points in space where abelian gauge fixing fails and magnetic monopoles are formed there. The ideas discussed in this ...