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Instantons, Topological Strings and Enumerative GeometryDec 08 2009Mar 12 2010We review and elaborate on certain aspects of the connections between instanton counting in maximally supersymmetric gauge theories and the computation of enumerative invariants of smooth varieties. We study in detail three instances of gauge theories ... More

Quantum Gravity, Field Theory and Signatures of Noncommutative SpacetimeJun 16 2009Oct 05 2009A pedagogical introduction to some of the main ideas and results of field theories on quantized spacetimes is presented, with emphasis on what such field theories may teach us about the problem of quantizing gravity. We examine to what extent noncommutative ... More

Microscopic Spectrum of the QCD Dirac Operator in Three DimensionsSep 28 2000Dec 05 2000The microscopic spectral correlators of the Dirac operator in three-dimensional Yang-Mills theory coupled to fundamental fermions and with three or more colours are derived from the supersymmetric formulation of partially quenched effective Lagrangians. ... More

Quantization of Higher Abelian Gauge Theory in Generalized Differential CohomologySep 12 2012Oct 01 2012We review and elaborate on some aspects of the quantization of certain classes of higher abelian gauge theories using techniques of generalized differential cohomology. Particular emphasis is placed on the examples of generalized Maxwell theory and Cheeger-Simons ... More

An Introduction to Nonassociative PhysicsMar 13 2019We give a pedagogical introduction to the nonassociative structures arising from recent developments in quantum mechanics with magnetic monopoles, in string theory and M-theory with non-geometric fluxes, and in M-theory with non-geometric Kaluza-Klein ... More

Perturbation Theory and TechniquesMay 16 2005May 27 2005Prepared for the Quantum Field Theory section of the Encyclopedia of Mathematical Physics, Elsevier, 2006. A brief introduction to the methodology and techniques of perturbative relativistic quantum field theory is presented.

Strings, Gauge Fields and MembranesMay 31 2004We present an overview of the intimate relationship between string and D-brane dynamics, and the dynamics of gauge and gravitational fields in three spacetime dimensions. The successes, prospects and open problems in describing both perturbative and nonperturbative ... More

String Holonomy and Extrinsic Geometry in Four-dimensional Topological Gauge TheoryApr 22 1998Jul 21 1998The most general gauge-invariant marginal deformation of four-dimensional abelian BF-type topological field theory is studied. It is shown that the deformed quantum field theory is topological and that its observables compute, in addition to the usual ... More

Equivariant Localization of Path IntegralsAug 12 1996We review equivariant localization techniques for the evaluation of Feynman path integrals. We develop systematic geometric methods for studying the semi-classical properties of phase space path integrals for dynamical systems, emphasizing the relations ... More

Matrix Models, Large N Limits and Noncommutative SolitonsDec 06 2005A survey of the interrelationships between matrix models and field theories on the noncommutative torus is presented. The discretization of noncommutative gauge theory by twisted reduced models is described along with a rigorous definition of the large ... More

Finite Volume Gauge Theory Partition Functions in Three DimensionsApr 25 2005Jun 20 2005We determine the fermion mass dependence of Euclidean finite volume partition functions for three-dimensional QCD in the epsilon-regime directly from the effective field theory of the pseudo-Goldstone modes by using zero-dimensional non-linear sigma-models. ... More

Quantum Field Theory on Noncommutative SpacesSep 20 2001Jan 23 2003A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner correspondence, noncommutative ... More

Topological Field Theory and Quantum Holonomy Representations of Motion GroupsAug 06 1999Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological extension of the ... More

Symmetry, Gravity and NoncommutativityJun 23 2006Jul 04 2006We review some aspects of the implementation of spacetime symmetries in noncommutative field theories, emphasizing their origin in string theory and how they may be used to construct theories of gravitation. The geometry of canonical noncommutative gauge ... More

D-branes and bivariant K-theorySep 17 2008We review various aspects of the topological classification of D-brane charges in K-theory, focusing on techniques from geometric K-homology and Kasparov's KK-theory. The latter formulation enables an elaborate description of D-brane charge on large classes ... More

D-Branes in Noncommutative Field TheoryDec 05 2005May 08 2007A mathematical introduction to the classical solutions of noncommutative field theory is presented, with emphasis on how they may be understood as states of D-branes in Type II superstring theory. Both scalar field theory and gauge theory on Moyal spaces ... More

Magnetic Backgrounds and Noncommutative Field TheoryJan 27 2004Feb 09 2004This paper is a rudimentary introduction, geared at non-specialists, to how noncommutative field theories arise in physics and their applications to string theory, particle physics and condensed matter systems.

An Introduction to Nonassociative PhysicsMar 13 2019Mar 31 2019We give a pedagogical introduction to the nonassociative structures arising from recent developments in quantum mechanics with magnetic monopoles, in string theory and M-theory with non-geometric fluxes, and in M-theory with non-geometric Kaluza-Klein ... More

Crystals, instantons and quantum toric geometryFeb 18 2011We describe the statistical mechanics of a melting crystal in three dimensions and its relation to a diverse range of models arising in combinatorics, algebraic geometry, integrable systems, low-dimensional gauge theories, topological string theory and ... More

D-Branes, Tachyons and K-HomologySep 25 2002Nov 12 2002We present an overview of the ways in which D-brane charges are classified in terms of K-theory, emphasizing the natural physical interpretations of a homological classification within a topological setting.

BUSSTEPP Lectures on String TheoryJul 15 2002This paper comprises the written version of the lectures on string theory delivered at the 31st British Universities Summer School on Theoretical Elementary Particle Physics which was held in Manchester, England, August 28 - September 12 2001.

Superconnections, Anomalies and Non-BPS Brane ChargesAug 07 2001Oct 09 2001The properties of brane-antibrane systems and systems of unstable D-branes in Type II superstring theory are investigated using the formalism of superconnections. The low-energy open string dynamics is shown to be probed by generalized Dirac operators. ... More

N=2 gauge theories, instanton moduli spaces and geometric representation theoryJul 02 2015Sep 24 2015We survey some of the AGT relations between N=2 gauge theories in four dimensions and geometric representations of symmetry algebras of two-dimensional conformal field theory on the equivariant cohomology of their instanton moduli spaces. We treat the ... More

Symmetries and Renormalization of Noncommutative Field TheoryJan 24 2007Feb 01 2007An overview of recent developments in the renormalization and in the implementation of spacetime symmetries of noncommutative field theory is presented, and argued to be intimately related.

Discrete Noncommutative Gauge TheoryJan 30 2001Feb 06 2001A review of the relationships between matrix models and noncommutative gauge theory is presented. A lattice version of noncommutative Yang-Mills theory is constructed and used to examine some generic properties of noncommutative quantum field theory, ... More

Quantization of Magnetic Poisson StructuresMar 07 2019We describe three perspectives on higher quantization, using the example of magnetic Poisson structures which embody recent discussions of nonassociativity in quantum mechanics with magnetic monopoles and string theory with non-geometric fluxes. We survey ... More

Propagators and Matrix Basis on Noncommutative Minkowski SpaceJun 30 2011Dec 09 2011We describe an analytic continuation of the Euclidean Grosse-Wulkenhaar and LSZ models which defines a one-parameter family of duality covariant noncommutative field theories interpolating between Euclidean and Minkowski space versions of these models, ... More

Chern-Simons matrix models, two-dimensional Yang-Mills theory and the Sutherland modelMar 05 2010Mar 29 2010We derive some new relationships between matrix models of Chern-Simons gauge theory and of two-dimensional Yang-Mills theory. We show that q-integration of the Stieltjes-Wigert matrix model is the discrete matrix model that describes q-deformed Yang-Mills ... More

Duality and Braiding in Twisted Quantum Field TheoryNov 09 2007Dec 10 2007We re-examine various issues surrounding the definition of twisted quantum field theories on flat noncommutative spaces. We propose an interpretation based on nonlocal commutative field redefinitions which clarifies previously observed properties such ... More

Teleparallel Gravity and Dimensional Reductions of Noncommutative Gauge TheoryMay 10 2001May 25 2001We study dimensional reductions of noncommutative electrodynamics on flat space which lead to gauge theories of gravitation. For a general class of such reductions, we show that the noncommutative gauge fields naturally yield a Weitzenbock geometry on ... More

Constructing D-Branes from K-TheoryJul 16 1999Aug 06 1999A detailed review of recent developments in the topological classification of D-branes in superstring theory is presented. Beginning with a thorough, self-contained introduction to the techniques and applications of topological K-theory, the relationships ... More

Brane Descent Relations in K-theoryApr 22 1999Jul 26 1999The various descent and duality relations among BPS and non-BPS D-branes are classified using topological K-theory. It is shown how the descent procedures for producing type-II D-branes from brane-antibrane bound states by tachyon condensation and $\klein$ ... More

Target Space Duality in Noncommutative GeometryJun 13 1997The structure of spacetime duality and discrete worldsheet symmetries of compactified string theory is examined within the framework of noncommutative geometry. The full noncommutative string spacetime is constructed using the Frohlich-Gawedzki spectral ... More

Covariant Quiver Gauge TheoriesApr 16 2014Apr 22 2014We consider dimensional reduction of gauge theories with arbitrary gauge group in a formalism based on equivariant principal bundles. For the classical gauge groups we clarify the relations between equivariant principal bundles and quiver bundles, and ... More

Extended quantum field theory, index theory and the parity anomalySep 12 2017Mar 29 2018We use techniques from functorial quantum field theory to provide a geometric description of the parity anomaly in fermionic systems coupled to background gauge and gravitational fields on odd-dimensional spacetimes. We give an explicit construction of ... More

Noncommutative gauge theories on D-branes in non-geometric backgroundsMar 12 2019We investigate the noncommutative gauge theories arising on the worldvolumes of D-branes in non-geometric backgrounds obtained by T-duality from twisted tori. We revisit the low-energy effective description of D-branes on three-dimensional T-folds, examining ... More

Localization for Yang-Mills Theory on the Fuzzy SphereJan 05 2007May 08 2007We present a new model for Yang-Mills theory on the fuzzy sphere in which the configuration space of gauge fields is given by a coadjoint orbit. In the classical limit it reduces to ordinary Yang-Mills theory on the sphere. We find all classical solutions ... More

Groupoid Quantization of Loop SpacesMar 27 2012We review the various contexts in which quantized 2-plectic manifolds are expected to appear within closed string theory and M-theory. We then discuss how the quantization of a 2-plectic manifold can be reduced to ordinary quantization of its loop space, ... More

Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-TheoryOct 15 2007Nov 20 2007We study D-branes and Ramond-Ramond fields on global orbifolds of Type II string theory with vanishing H-flux using methods of equivariant K-theory and K-homology. We illustrate how Bredon equivariant cohomology naturally realizes stringy orbifold cohomology. ... More

Dimensional reduction over the quantum sphere and non-abelian q-vorticesMar 10 2010Oct 19 2011We extend equivariant dimensional reduction techniques to the case of quantum spaces which are the product of a Kaehler manifold M with the quantum two-sphere. We work out the reduction of bundles which are equivariant under the natural action of the ... More

Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge TheoryJan 30 2007We use twist deformation techniques to analyse the behaviour under area-preserving diffeomorphisms of quantum averages of Wilson loops in Yang-Mills theory on the noncommutative plane. We find that while the classical gauge theory is manifestly twist ... More

Noncommutative Geometry and String DualityApr 08 1999A review of the applications of noncommutative geometry to a systematic formulation of duality symmetries in string theory is presented. The spectral triples associated with a lattice vertex operator algebra and the corresponding Dirac-Ramond operators ... More

Curve counting, instantons and McKay correspondencesSep 07 2012Feb 20 2013We survey some features of equivariant instanton partition functions of topological gauge theories on four and six dimensional toric Kahler varieties, and their geometric and algebraic counterparts in the enumerative problem of counting holomorphic curves. ... More

Two-dimensional Yang-Mills theory, Painleve equations and the six-vertex modelFeb 17 2011Feb 13 2012We show that the chiral partition function of two-dimensional Yang-Mills theory on the sphere can be mapped to the partition function of the homogeneous six-vertex model with domain wall boundary conditions in the ferroelectric phase. A discrete matrix ... More

Noncommutative Field Theory on Homogeneous Gravitational WavesFeb 03 2006Feb 16 2006We describe an algebraic approach to the time-dependent noncommutative geometry of a six-dimensional Cahen-Wallach pp-wave string background supported by a constant Neveu-Schwarz flux, and develop a general formalism to construct and analyse quantum field ... More

Nonassociative Field Theory on Non-Geometric SpacesApr 29 2014We describe quasi-Hopf twist deformations of flat closed string compactifications with non-geometric R-flux using a suitable cochain twist, and construct nonassociative deformations of fields and differential calculus. We report on our new findings in ... More

Branes, Quantization and Fuzzy SpheresJan 31 2011We propose generalized quantization axioms for Nambu-Poisson manifolds, which allow for a geometric interpretation of n-Lie algebras and their enveloping algebras. We illustrate these axioms by describing extensions of Berezin-Toeplitz quantization to ... More

Duality covariant quantum field theory on noncommutative Minkowski spaceOct 07 2008Feb 10 2009We prove that a scalar quantum field theory defined on noncommutative Minkowski spacetime with noncommuting momentum coordinates is covariant with respect to the UV/IR duality which exchanges coordinates and momenta. The proof is based on suitable resonance ... More

Noncommutative Geometry and Spacetime Gauge Symmetries of String TheoryDec 22 1997We illustrate the various ways in which the algebraic framework of noncommutative geometry naturally captures the short-distance spacetime properties of string theory. We describe the noncommutative spacetime constructed from a vertex operator algebra ... More

Fluxes, bundle gerbes and 2-Hilbert spacesDec 06 2016We elaborate on the construction of a prequantum 2-Hilbert space from a bundle gerbe over a 2-plectic manifold, providing the first steps in a program of higher geometric quantisation of closed strings in flux compactifications and of M5-branes in C-fields. ... More

Nonabelian localization for gauge theory on the fuzzy sphereAug 31 2007Sep 13 2007We apply nonabelian equivariant localization techniques to Yang-Mills theory on the fuzzy sphere to write the partition function entirely as a sum over local contributions from critical points of the action. The contributions of the classical saddle-points ... More

Electric-magnetic Duality in Noncommutative GeometrySep 28 1997The structure of S-duality in U(1) gauge theory on a 4-manifold M is examined using the formalism of noncommutative geometry. A noncommutative space is constructed from the algebra of Wilson-'t Hooft line operators which encodes both the ordinary geometry ... More

UV/IR duality in noncommutative quantum field theoryJan 21 2010Jun 16 2010We review the construction of renormalizable noncommutative euclidean phi(4)-theories based on the UV/IR duality covariant modification of the standard field theory, and how the formalism can be extended to scalar field theories defined on noncommutative ... More

Isometric Embeddings and Noncommutative Branes in Homogeneous Gravitational WavesFeb 04 2005Feb 28 2005We characterize the worldvolume theories on symmetric D-branes in a six-dimensional Cahen-Wallach pp-wave supported by a constant Neveu-Schwarz three-form flux. We find a class of flat noncommutative euclidean D3-branes analogous to branes in a constant ... More

Quantization of 2-Plectic ManifoldsJun 09 2011We describe an extension of the axioms of quantization to the case of 2-plectic manifolds. We show how such quantum spaces can be obtained as stable classical solutions in a zero-dimensional 3-algebra reduced model obtained by dimensional reduction of ... More

q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinementMay 07 2013Aug 05 2013We characterise the quantum group gauge symmetries underlying q-deformations of two-dimensional Yang-Mills theory by studying their relationships with the matrix models that appear in Chern-Simons theory and six-dimensional N=2 gauge theories, together ... More

't Hooft anomalies of discrete gauge theories and non-abelian group cohomologyNov 13 2018We study discrete symmetries of Dijkgraaf-Witten theories and their gauging in the framework of (extended) functorial quantum field theory. Non-abelian group cohomology is used to describe discrete symmetries and we derive concrete conditions for such ... More

Reduced Chern-Simons Quiver Theories and Cohomological 3-Algebra ModelsJul 05 2013We study the BPS spectrum and vacuum moduli spaces in dimensional reductions of Chern-Simons-matter theories with N>=2 supersymmetry to zero dimensions. Our main example is a matrix model version of the ABJM theory which we relate explicitly to certain ... More

Duality in Scalar Field Theory on Noncommutative Phase SpacesFeb 06 2002Feb 27 2002We describe a novel duality symmetry of Phi(4)-theory defined on noncommutative Euclidean space and with noncommuting momentum coordinates. This duality acts on the fields by Fourier transformation and scaling. It is an extension, to interactions defined ... More

Groupoids, Loop Spaces and Quantization of 2-Plectic ManifoldsNov 02 2012Nov 26 2012We describe the quantization of 2-plectic manifolds as they arise in the context of the quantum geometry of M-branes and non-geometric flux compactifications of closed string theory. We review the groupoid approach to quantizing Poisson manifolds in detail, ... More

Matrix models and stochastic growth in Donaldson-Thomas theoryMay 31 2010Aug 10 2012We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood ... More

Triproducts, nonassociative star products and geometry of R-flux string compactificationsApr 15 2015We elucidate relations between different approaches to describing the nonassociative deformations of geometry that arise in non-geometric string theory. We demonstrate how to derive configuration space triproducts exactly from nonassociative phase space ... More

Topological Navigation of Simulated Robots using Occupancy GridNov 08 2004Formerly I presented a metric navigation method in the Webots mobile robot simulator. The navigating Khepera-like robot builds an occupancy grid of the environment and explores the square-shaped room around with a value iteration algorithm. Now I created ... More

Membrane Sigma-Models and Quantization of Non-Geometric Flux BackgroundsJul 04 2012Jul 25 2012We develop quantization techniques for describing the nonassociative geometry probed by closed strings in flat non-geometric R-flux backgrounds M. Starting from a suitable Courant sigma-model on an open membrane with target space M, regarded as a topological ... More

Nonassociative geometry and twist deformations in non-geometric string theoryFeb 28 2014We describe nonassociative deformations of geometry probed by closed strings in non-geometric flux compactifications of string theory. We show that these non-geometric backgrounds can be geometrised through the dynamics of open membranes whose boundaries ... More

Matrix D-brane Dynamics, Logarithmic Operators and Quantization of Noncommutative SpacetimeAug 20 1998We describe the structure of the moduli space of $\sigma$-model couplings for the worldsheet description of a system of $N$ D-particles, in the case that the couplings are represented by a pair of logarithmic recoil operators. We derive expressions for ... More

Gradient Flow in Logarithmic Conformal Field TheoryMar 11 1998Apr 16 1998We establish conditions under which the worldsheet beta-functions of logarithmic conformal field theories can be derived as the gradient of some scalar function on the moduli space of running coupling constants. We derive a renormalization group invariant ... More

Matrix Strings in Two-dimensional Yang-Mills TheoryMar 29 1997We describe the structure of string vacuum states in the supersymmetric matrix model for M theory compactified on a circle in the large-N limit. We show that the theory admits topological instanton field configurations which at short-distance scales reduce ... More

Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theoryMar 28 2008Sep 17 2008We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its partition function ... More

Refined Chern-Simons theory and (q,t)-deformed Yang-Mills theory: Semi-classical expansion and planar limitJun 07 2013We study the relationship between refined Chern-Simons theory on lens spaces S^3/Z_p and (q,t)-deformed Yang-Mills theory on the sphere S^2. We derive the instanton partition function of (q,t)-deformed U(N) Yang-Mills theory and describe it explicitly ... More

Dimensional Reduction and Vacuum Structure of Quiver Gauge TheoryMay 29 2009Nov 02 2011We describe the structure of the vacuum states of quiver gauge theories obtained via dimensional reduction over homogeneous spaces, in the explicit example of SU(3)-equivariant dimensional reduction of Yang-Mills-Dirac theory on manifolds of the form ... More

Black String Entropy from Anomalous D-brane CouplingsMay 05 1998Sep 09 1998The quantum corrections to the counting of statistical entropy for the 5+1-dimensional extremal black string in type-IIB supergravity with two observers are studied using anomalous Wess-Zumino actions for the corresponding intersecting D-brane description. ... More

Fermionic Matrix ModelsMay 21 1996Nov 07 1996We review a class of matrix models whose degrees of freedom are matrices with anticommuting elements. We discuss the properties of the adjoint fermion one-, two- and gauge invariant D-dimensional matrix models at large-N and compare them with their bosonic ... More

Quiver Gauge Theory of Nonabelian Vortices and Noncommutative Instantons in Higher DimensionsApr 04 2005Feb 16 2006We construct explicit BPS and non-BPS solutions of the Yang-Mills equations on the noncommutative space R^{2n}_\theta x S^2 which have manifest spherical symmetry. Using SU(2)-equivariant dimensional reduction techniques, we show that the solutions imply ... More

Spectral Geometry of Heterotic CompactificationsDec 27 1998The structure of heterotic string target space compactifications is studied using the formalism of the noncommutative geometry associated with lattice vertex operator algebras. The spectral triples of the noncommutative spacetimes are constructed and ... More

Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum MechanicsDec 05 2013Oct 24 2014We analyse the symmetries underlying nonassociative deformations of geometry in non-geometric R-flux compactifications which arise via T-duality from closed strings with constant geometric fluxes. Starting from the non-abelian Lie algebra of translations ... More

Supersymmetric gauge theories, Coulomb gases and Chern-Simons matrix modelsOct 11 2013Oct 22 2013We develop Coulomb gas pictures of strong and weak coupling regimes of supersymmetric Yang-Mills theory in five and four dimensions. By relating them to the matrix models that arise in Chern-Simons theory, we compute their free energies in the large N ... More

Non-linear Schroedinger Dynamics of Matrix D-branesSep 19 1999May 30 2000We formulate an effective Schroedinger wave equation describing the quantum dynamics of a system of D0-branes by applying the Wilson renormalization group equation to the worldsheet partition function of a deformed sigma-model describing the system, which ... More

AGT relations for abelian quiver gauge theories on ALE spacesMay 27 2014Mar 02 2016We construct level one dominant representations of the affine Kac-Moody algebra $\widehat{\mathfrak{gl}}_k$ on the equivariant cohomology groups of moduli spaces of rank one framed sheaves on the orbifold compactification of the minimal resolution $X_k$ ... More

Solitons and Yukawa Couplings in Nearly Kahler Flux CompactificationsAug 05 2012Aug 18 2013We study vacuum states and symmetric fermions in equivariant dimensional reduction of Yang-Mills-Dirac theory over the six-dimensional homogeneous space SU(3)/U(1)x U(1) endowed with a family of SU(3)-structures including a nearly Kahler structure. We ... More

Instantons, Quivers and Noncommutative Donaldson-Thomas TheoryDec 13 2010Aug 22 2011We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analysing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes ... More

Instantons and Donaldson-Thomas InvariantsApr 07 2008We review some recent progress in understanding the relation between a six dimensional topological Yang-Mills theory and the enumerative geometry of Calabi-Yau threefolds. The gauge theory localizes on generalized instanton solutions and is conjecturally ... More

Equivariant Dimensional Reduction and Quiver Gauge TheoriesJan 14 2010We review recent applications of equivariant dimensional reduction techniques to the construction of Yang-Mills-Higgs-Dirac theories with dynamical mass generation and exactly massless chiral fermions.

Geometric K-Homology of Flat D-BranesJul 05 2005Nov 21 2005We use the Baum-Douglas construction of K-homology to explicitly describe various aspects of D-branes in Type II superstring theory in the absence of background supergravity form fields. We rigorously derive various stability criteria for states of D-branes ... More

Differential cohomology and locally covariant quantum field theoryJun 05 2014Dec 08 2016We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental ... More

Matrix Quantum Mechanics and Soliton Regularization of Noncommutative Field TheoryJan 12 2004Jan 20 2004We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is applied to the ... More

A New Matrix Model for Noncommutative Field TheorySep 02 2003We describe a new regularization of quantum field theory on the noncommutative torus by means of one-dimensional matrix models. The construction is based on the Elliott-Evans inductive limit decomposition of the noncommutative torus algebra. The matrix ... More

Two-Loop String Theory on Null CompactificationsJan 30 2006We compute the two-loop contributions to the free energy in the null compactification of perturbative string theory at finite temperature. The cases of bosonic, Type II and heterotic strings are all treated. The calculation exploits an explicit reductive ... More

Instantons, Fluxons and Open Gauge String TheoryNov 30 2004We use the exact instanton expansion to illustrate various string characteristics of noncommutative gauge theory in two dimensions. We analyse the spectrum of the model and present some evidence in favour of Hagedorn and fractal behaviours. The decompactification ... More

D-Brane Dynamics and Logarithmic Superconformal AlgebrasJun 27 2001Oct 23 2001We construct the consistent supersymmetric extensions of the operators describing the recoil of a D-brane and show that they realize an N=1 logarithmic superconformal algebra. The corresponding supersymmetric vertex operator is related to the action of ... More

D-branes and the Non-commutative Structure of Quantum SpacetimeNov 12 1998A worldsheet approach to the study of non-abelian D-particle dynamics is presented based on viewing matrix-valued D-brane coordinate fields as coupling constants of a deformed sigma-model which defines a logarithmic conformal field theory. The short-distance ... More

Spacetime Quantization from Non-abelian D-particle DynamicsJul 25 1998We 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 worldsheet $\sigma$-model. We show that the Zamolodchikov metric on the associated moduli ... More

Liouville Dressed Weights and Renormalization of Spin in Topologically Massive GravityMar 10 1997We examine the relations between observables in two- and three-dimensional quantum gravity by studying the coupling of topologically massive gravity to matter fields in non-trivial representations of the three-dimensional Lorentz group. We show that the ... More

Polymer Statistics and Fermionic Vector ModelsFeb 01 1996Mar 04 1996We consider a variation of $O(N)$-symmetric vector models in which the vector components are Grassmann numbers. We show that these theories generate the same sort of random polymer models as the $O(N)$ vector models and that they lie in the same universality ... More

Equivariant Localization, Spin Systems and Topological Quantum Theory on Riemann SurfacesJun 18 1994We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show that the localized ... More

Phase Space Isometries and Equivariant Localization of Path Integrals in Two DimensionsNov 23 1993By considering the most general metric which can occur on a contractable two dimensional symplectic manifold, we find the most general Hamiltonians on a two dimensional phase space to which equivariant localization formulas for the associated path integrals ... More

Double quiver gauge theory and nearly Kahler flux compactificationsSep 16 2010Feb 13 2012We consider G-equivariant dimensional reduction of Yang-Mills theory with torsion on manifolds of the form MxG/H where M is a smooth manifold, and G/H is a compact six-dimensional homogeneous space provided with a never integrable almost complex structure ... More

Quantized Nambu-Poisson Manifolds and n-Lie AlgebrasJan 19 2010Feb 18 2010We investigate the geometric interpretation of quantized Nambu-Poisson structures in terms of noncommutative geometries. We describe an extension of the usual axioms of quantization in which classical Nambu-Poisson structures are translated to n-Lie algebras ... More

Algebraic deformations of toric varieties I. General constructionsJan 08 2010Jun 27 2013We construct and study noncommutative deformations of toric varieties by combining techniques from toric geometry, isospectral deformations, and noncommutative geometry in braided monoidal categories. Our approach utilizes the same fan structure of the ... More

Algebraic deformations of toric varieties II. Noncommutative instantonsJun 28 2011Sep 18 2012We continue our study of the noncommutative algebraic and differential geometry of a particular class of deformations of toric varieties, focusing on aspects pertinent to the construction and enumeration of noncommutative instantons on these varieties. ... More