\(q\)-deformations of two-dimensional Yang-Mills theory: classification, categorification and refinement

DOI10.1016/j.nuclphysb.2013.08.001zbMath1284.81173arXiv1305.1580OpenAlexW2104300153MaRDI QIDQ2440210

Richard J. Szabo, Miguel Tierz

Publication date: 27 March 2014

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.1580

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Supersymmetric field theories in quantum mechanics (81T60) Yang-Mills and other gauge theories in quantum field theory (81T13) Eta-invariants, Chern-Simons invariants (58J28) Grothendieck groups (category-theoretic aspects) (18F30)

Related Items

Wilson punctured network defects in 2D \(q\)-deformed Yang-Mills theory, 3d-3d correspondence revisited, \( T\overline{T} \)-deformation of \(q\)-Yang-Mills theory, Quantum exponentials for the modular double and applications in gravity models, On irregular singularity wave functions and superconformal indices, Torus knot polynomials and Susy Wilson loops, Large \(N\) phase transition in \( T\overline{T} \) -deformed \(2d\) Yang-Mills theory on the sphere, Chern–Simons theory encoded on a spin chain, Refined Chern-Simons theory and \((q, t)\)-deformed Yang-Mills theory: semi-classical expansion and planar limit, Five-dimensional cohomological localization and squashed \(q\)-deformations of two-dimensional Yang-Mills theory, From quantum groups to Liouville and dilaton quantum gravity, Global and local scaling limits for the β = 2 Stieltjes–Wigert random matrix ensemble, Supersymmetric \(U(N)\) Chern-Simons-matter theory and phase transitions

Cites Work

• Quantum field theory on noncommutative spaces
• Lectures on \(2\)D Yang-Mills theory, equivariant cohomology and topological field theories
• The formulae of Kontsevich and Verlinde from the perspective of the Drinfeld double.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bootstrapping the superconformal index with surface defects
• Refined black hole ensembles and topological strings
• On S-duality of the superconformal index on Lens spaces and 2d TQFT
• M5-branes from gauge theories on the 5-sphere
• Refined Hopf link revisited
• Schur-finiteness in \(\lambda \)-rings
• Topological recursion and mirror curves
• Volume conjecture: refined and categorified
• Localization for Wilson loops in Chern-Simons theory
• Quantum foam and topological strings
• Wall crossing, open BPS counting and matrix models
• Cardy algebras and sewing constraints. I
• Instantons, topological strings, and enumerative geometry
• Wall crossing as seen by matrix models
• Branes, black holes and topological strings on toric Calabi-Yau manifolds
• Dimensional reduction over the quantum sphere and non-Abelian \(q\)-vortices
• Abelian current algebra and the Virasoro algebra on the lattice
• Field theory on the \(q\)-deformed fuzzy sphere. II: Quantization
• Seiberg-Witten prepotential from instanton counting
• Surface defects, the superconformal index and \(q\)-deformed Yang-Mills
• BPS states, crystals, and matrices
• Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants
• On the averages of characteristic polynomials from classical groups
• Black holes, \(q\)-deformed 2d Yang--Mills, and non-perturbative topological strings
• Discrete and oscillatory matrix models in Chern--Simons theory
• Hyperdeterminantal expressions for Jack functions of rectangular shapes
• Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
• Symmetric obstruction theories and Hilbert schemes of points on threefolds
• Instanton partition functions and M-theory
• Quantum spheres
• On generalized Stieltjes-Wigert and related orthogonal polynomials
• On quantum gauge theories in two dimensions
• Two dimensional gauge theories revisited
• The triple, quintuple and setuple product identities revisited
• From discrete to absolutely continuous solutions of indeterminate moment problems
• Quantum group gauge theory on quantum spaces
• Asymptotic expansions for \(q\)-gamma, \(q\)-exponential, and \(q\)-Bessel functions
• Module categories, weak Hopf algebras and modular invariants
• Instanton expansion of noncommutative gauge theory in two dimensions
• The string theory approach to generalized \(2\)D Yang-Mills theory
• Relativistic Calogero-Moser model as gauged WZW theory.
• A path integral approach to the Kontsevich quantization formula.
• Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras
• TFT construction of RCFT correlators. I: Partition functions
• The moment problem associated with the Stieltjes-Wigert polynomials
• Macdonald's polynomials and representations of quantum groups
• On diagonalization in map(\(M\),G)
• Combinatorial quantization of the Hamiltonian Chern-Simons theory. I
• Spherical functions on affine Lie groups
• Two dimensional lattice gauge theory based on a quantum group
• The remodeling conjecture and the Faber-Pandharipande formula
• Gauge theories and Macdonald polynomials
• Instanton counting and wall-crossing for orbifold quivers
• 5D SYM and 2D \(q\)-deformed YM
• Hodge integrals and Gromov-Witten theory
• Black holes, instanton counting on toric singularities and \(q\)-deformed two-dimensional Yang-Mills theory
• BPS microstates and the open topological string wave function
• Large \(N\) expansion of \(q\)-deformed two-dimensional Yang-Mills theory and Hecke algebras
• Non-abelian localization for Chern-Simons theory
• Counting formulas associated with some random matrix averages
• Knot homology and refined Chern-Simons index
• Melting crystal, quantum torus and Toda hierarchy
• \(q\)-Selberg integrals and Macdonald polynomials
• LOOP AVERAGES AND PARTITION FUNCTIONS IN U(N) GAUGE THEORY ON TWO-DIMENSIONAL MANIFOLDS
• Matrix models and stochastic growth in Donaldson-Thomas theory
• MACDONALD PROCESSES
• Geometry and Combinatorics of Crystal Melting
• Intersection Pairings on Spaces of Connections and Chern-Simons Theory on Seifert Manifolds
• REFINED BPS STATE COUNTING FROM NEKRASOV'S FORMULA AND MACDONALD FUNCTIONS
• The importance of the Selberg integral
• Chern–Simons matrix models, two-dimensional Yang–Mills theory and the Sutherland model
• Essays on the theory of elliptic hypergeometric functions
• Toeplitz Matrices Generated by the Laurent Series Expansion of an Arbitrary Rational Function
• On Cherednik-Macdonald-Mehta identities
• Tensor Structures Arising from Affine Lie Algebras. IV
• A simple difference realization of the Heisenberg q-algebra
• The Hopf algebra structure of the character rings of classical groups
• 4d partition function on S1 × S3 and 2d Yang–Mills with nonzero area
• The local Gromov-Witten theory of curves
• Moments of characteristic polynomials for compact symmetric spaces and Jack polynomials
• Categories and Sheaves
• A Characterization and a Class of Distribution Functions for the Stieltjes-Wigert Polynomials
• On an inner product in modular tensor categories
• SOFT MATRIX MODELS AND CHERN–SIMONS PARTITION FUNCTIONS