Topological quantum field theory

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DOI10.1007/BF01223371zbMath0656.53078WikidataQ55880680 ScholiaQ55880680MaRDI QIDQ1110122

Edward Witten

Publication date: 1988

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Floer homology supersymmetric gauge theory stress tensor twistor Floer theory Donaldson polynomial invariants

Mathematics Subject Classification ID

Supersymmetric field theories in quantum mechanics (81T60) Constructive quantum field theory (81T08) Applications of global differential geometry to the sciences (53C80)

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I: 4-dimensional pure gauge theory, TOPOLOGICAL HYPERMULTIPLET ON N = 2 TWISTED SUPERSPACE IN FOUR DIMENSIONS, CLASSICAL SOLUTIONS TO YANG–MILLS–CHERN–SIMONS FIELD COUPLED TO AN EXTERNAL SOURCE, Conformal Field Theory as a Nuclear Functor, Witten complex and supersymmetric quantum mechanics on SO(3), Seiberg-Witten equations in R4: Lie symmetries, particular solutions, integrability, Partition functions of supersymmetric gauge theories in noncommutative R2D and their unified perspective, Fivebranes and 4-Manifolds, Supersymmetric partition functions on Riemann surfaces, HODGE TYPE COHOMOLOGICAL GAUGE THEORIES, The monopole equations in topological Yang–Mills, Cabled Wilson loops in BF theories, The Lax pair by dimensional reduction of Chern–Simons gauge theory, WHAT DO TOPOLOGISTS WANT FROM SEIBERG–WITTEN THEORY?, 4-Manifold topology, Donaldson–Witten theory, Floer homology and higher gauge theory methods in the BV-BFV formalism, Gauge Fields in Physics and Mathematics, Topological aspects of the critical three-state Potts model, Characteristic Classes, Top down approach to 6D SCFTs, Conserved chiral currents on the boundary of 3D Maxwell theory, Index of the transversally elliptic complex in Pestunization, SU(2)₀ AND OSp(2|2)_-2 WZNW MODELS: TWO CURRENT ALGEBRAS, ONE LOGARITHMIC CFT, Finite features of quantum de Sitter space, Roadmap on Wilson loops in 3d Chern–Simons-matter theories, OBSERVATIONS ON A U(1) × U(1) VECTOR THEORY, SOLUTIONS OF VANISHING CURVATURE NON-ABELIAN MONOPOLE EQUATIONS, The impact of Thom’s cobordism theory, Yang–Mills theories on geometric spaces, COHOMOLOGICAL GAUGE THEORIES IN D > 4 WITH SPECIAL HOLONOMY Spin(7) AND G₂, QFT, STRINGS AND LOW-DIMENSIONAL TOPOLOGY, Noncommutative cohomological field theory and GMS soliton, A new realization for the d=2 topological algebra, Equivariance, BRST symmetry, and superspace, Matching renormalization schemes in holography, Chern-Simons theory and knot invariants, Lectures on knot homology and quantum curves, Equivariant homology, Introduction to localization in quantum field theory, Review of localization in geometry, Supersymmetric localization in two dimensions, An introduction to supersymmetric field theories in curved space, Localization on three-dimensional manifolds, TheF-theorem andF-maximization, ${{{\mathcal N}}=2}$ SUSY gauge theories on S⁴, State sum invariants of three manifolds from spherical multi-fusion categories, Some novel features in 2D non-Abelian theory: BRST approach, Five Lectures on Topological Field Theory, Quantum theory and geometry, Topological BF theories in 3 and 4 dimensions, Clock and category: Is quantum gravity algebraic?, Outline of a generally covariant quantum field theory and a quantum theory of gravity, Localization and diagonalization: A review of functional integral techniques for low-dimensional gauge theories and topological field theories, Topological Yang–Mills theory from non-commutative geometry, Holomorphic field theories and Calabi–Yau algebras, Non-Abelian BF theory for 2 + 1 dimensional topological states of matter, Three-dimensional dynamics of four-dimensional topological BF theory with boundary, The Seiberg-Witten equations and 4-manifold topology, Quantum simulation of non-trivial topology, N=2 SUPER-YANG–MILLS ACTION AND BRST COHOMOLOGY, A hierarchy of topological tensor network states, Information from quantum blackhole physics, SUPERSYMMETRIC YANG–MILLS THEORIES WITH EXACT SUPERSYMMETRY ON THE LATTICE, Bordered Heegaard Floer homology, The knot invariant Υ using grid homologies, NEAR-EXTREMAL BLACK BRANES WITH n³ ENTROPY GROWTH, Lectures on \(2\)D Yang-Mills theory, equivariant cohomology and topological field theories, Lectures on four-manifolds and topological gauge theories, Lectures on special Kähler geometry and electric-magnetic duality rotations, Four-dimensional avatars of two-dimensional RCFT, Reduction, Donaldson invariants and quantum cohomology ring, On the identification of observables in topological gauge models, Topological Yang-Mills symmetry, String duality, automorphic forms, and generalized Kac-Moody algebras, Integrating over the Coulomb branch in \({\mathcal N}=2\) gauge theory, DIFFERENTIAL GEOMETRY FROM QUANTUM FIELD THEORY, 0 + 1-DIMENSIONAL TQFT: FROM HILBERT VECTOR SPACE TO TANGLE CATEGORY, The Cobordism hypothesis, Holomorphic analogs of topological gauge theories, Multi-instantons, supersymmetry and topological field theories, Cohomological Yang-Mills theories on Kähler 3-folds, Constructing New Quasitriangular Turaev Group Coalgebras, Quantum field theory on noncommutative spaces, INTEGRABLE SYSTEMS IN ONE AND TWO DIMENSIONS AND REDUCED TOPOLOGICAL GAUGE THEORIES, EXACT RESULTS IN GAUGE THEORIES: PUTTING SUPERSYMMETRY TO WORK, BOGOMOL'NYI VORTICES FROM SEIBERG–WITTEN MONOPOLES, COHOMOLOGICAL FIELD THEORY APPROACH TO MATRIX STRINGS, Nonperturbative two-body dynamics in 2+1-dimensional gravity, VOA[M4], Geometrical interpretation of BRST symmetry in topological Yang–Mills–Higgs theory, A CANONICAL ANALYSIS OF THE EINSTEIN–HILBERT IN FIRST ORDER FORM, Notes on Topological Quantum Field Theories, Geometry and physics: An overview, The holomorphic bosonic string, HOMOTOPY QUANTUM FIELD THEORIES AND THE HOMOTOPY COBORDISM CATEGORY IN DIMENSION 1 + 1, Dualizable tensor categories, Becchi-Rouet-Stora-Tyutin cohomology of compact gauge algebras, Suppression of local degrees of freedom of gauge fields by chiral anomalies, Link invariants for flows in higher dimensions, Computer tests of Witten’s Chern-Simons theory against the theory of three-manifolds, Semirigid supergravity, Spontaneous breaking of topological symmetry, The osp(1,2)-covariant Lagrangian quantization of reducible massive gauge theories, Extended TQFTs from non-semisimple modular categories, Einstein2: Brownian Motion Meets General Relativity, 𝒩 = 4 supersymmetric quantum mechanical model: Novel symmetries, 3d TQFTs from Argyres–Douglas theories, A slow review of the AGT correspondence, SUSY localization for Coulomb branch operators in omega-deformed 3d \(\mathcal{N} = 4\) gauge theories, D4-branes wrapped on four-dimensional orbifolds through consistent truncation, Vertex operator algebras and topologically twisted Chern-Simons-matter theories, Erratum to: ``Supersymmetric localization: \(\mathcal{N} = (2, 2)\) theories on \(\mathrm{S}^2\) and \(\mathrm{AdS}_2\), Effective gravitational couplings of Kaluza-Klein gauge theories, A Goldstone theorem for continuous non-invertible symmetries, Integrability and BRST invariance from BF topological theory, Vertex algebra of extended operators in 4d \(N=2\) superconformal field theories. I., Double Field Theory for the A/B‐Models and Topological S‐Duality in Generalized Geometry, Connectomes and properties of quantum entanglement, From 5d flat connections to 4d fluxes (the art of slicing the cone), F‐theory and Dark Energy, Sequential Measurements, Topological Quantum Field Theories, and Topological Quantum Neural Networks, Catégorification et méthode, KHOVANOV SPECTRA FOR TANGLES, ADHM in \(8d\), coloured solid partitions and Donaldson-Thomas invariants on orbifolds, Applications of quantum representations of mapping class groups, Interfaces and quantum algebras. I: Stable envelopes, Quantum gases on a torus, Localization theorem for homological vector fields, Towards equivariant Yang-Mills theory, Knots, Diagrams and Kids’ Shoelaces. On Space and their Forms, Twisted eleven-dimensional supergravity, D4-branes wrapped on a topological disk, Covariant star product on semi-conformally flat noncommutative Calabi–Yau manifolds and noncommutative topological index theorem, Knot homologies and generalized quiver partition functions, Twisted holography and celestial holography from boundary chiral algebra, Chern–Simons field theory on the general affine group, 3d-gravity and the extension of Cartan connections, Twisted formalism for 3d \(\mathcal{N}=4\) theories, The Duflo-Serganova functor, vingt ans après, Correlation functions in topological Yang-Mills theory with two fermionic charges, 4-dimensional BF gravity on the lattice, Some properties of models exhibiting gauge and curvature ladders, Analytic loops and gauge fields, Integrable many-body systems and gauge theories, On the multi-instanton measure for super Yang-Mills theories, Protected operators in N=2,4 supersymmetric theories, Topological DBI actions and nonlinear instantons, \(N_T=4\) equivariant extension of the 3D topological model of Blau and Thompson, Higgs bundles and four manifolds, Tannaka duality for Maschkean categories, \(\operatorname{SL}(2, \mathbb{C})\) Chern-Simons theory, a non-planar graph operator, and 4D quantum gravity with a cosmological constant: semiclassical geometry

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