A Strong Coupling Test of S-Duality

Abstract

By studying the partition function of $N=4$ topologically twisted supersymmetric Yang-Mills on four-manifolds, we make an exact strong coupling test of the Montonen-Olive strong-weak duality conjecture. Unexpected and exciting links are found with two-dimensional rational conformal field theory.

114 pages (some minor changes)

References in corpus (2)

• Duality Symmetries of 4D Heterotic Strings
• Non-Abelian Strong-Weak Coupling Duality in (String-Derived) N=4 Supersymmetric Yang-Mills Theories

Cited by in corpus (471)

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• GUTs and Exceptional Branes in F-theory - I
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• The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD
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• Instantons on ALE spaces and orbifold partitions
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• A TOPOLOGICAL LAGRANGIAN FOR MONOPOLES ON FOUR-MANIFOLDS
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• Noncommutative instantons revisited
• A Combinatorial Study on Quiver Varieties
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• Supersymmetric localization in two dimensions
• QCD, Supersymmetric QCD, Lattice QCD and String Theory: Synthesis on the Horizon?
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• A Test Of The Chiral E8 Current Algebra On A 6D Non-Critical String
• Reflections on the Matter of 3d $\mathcal{N}=1$ Vacua and Local $Spin(7)$ Compactifications
• Exact Electric-Magnetic Duality in N=2 Supersymmetric QCD Theories
• Monopole contributions to refined Vafa-Witten invariants
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• Non-Abelian Monopoles on Four-Manifolds
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• Supersymmetric Yang--Mills theories with exact supersymmetry on the lattice
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• On twisted N=2 5D super Yang-Mills theory
• Topological Chern-Simons Sigma Model
• Branes, Black Holes and Topological Strings on Toric Calabi-Yau Manifolds
• Surface defects in gauge theory and KZ equation
• Black-holes, topological strings and large N phase transitions
• Hodge Duality and Cosmological Constant
• S-Duality and Helicity Amplitudes
• Remarks on Non-Abelian Duality in N=1 Supersymmetric Gauge Theories
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• Quantum toroidal algebras and solvable structures in gauge/string theory
• Topological twists of supersymmetric algebras of observables
• Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities
• Vafa-Witten theory and iterated integrals of modular forms
• Examples of M5-Brane Elliptic Genera
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• Instantons, supersymmetric vacua, and emergent geometries
• Matrix Description of (1,0) Theories in Six Dimensions
• Seiberg-Witten Monopole Equations on Noncommutative R^4
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• Conformal topological Yang-Mills theory and de Sitter holography
• N=1* vacua, Fuzzy Spheres and Integrable Systems
• Electric-magnetic Duality and Deformations of Three-Dimensional CFT's
• N=1 Dualities for Exceptional Gauge Groups and Quantum Global Symmetries
• Duality in twisted N=4 supersymmetric gauge theories in four dimensions
• Duality and Mock Modularity
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• Donaldson-Witten theory and indefinite theta functions
• Variations on stability
• Confinement, brane symmetry and the Julia-Toulouse approach for condensation of defects
• Compact T-branes
• Crystal melting on toric surfaces
• The Bullough-Dodd model coupled to matter fields
• Holographic dual of hot Polchinski-Strassler quark-gluon plasma
• Topological AdS/CFT
• Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
• Ground States of S-duality Twisted N=4 Super Yang-Mills Theory
• Renormalization and BRST symmetry in Donaldson-Witten theory
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• Modular Anomaly from Holomorphic Anomaly in Mass Deformed N=2 Superconformal Field Theories
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• From strings in 6d to strings in 5d
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• Heterotic-Type IIA Duality and Degenerations of K3 Surfaces
• Effective gravitational couplings of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories
• Integrable theories in any dimension and homogenous spaces
• String Theory Duals for Mass-deformed SO(N) and USp(2N) N=4 SYM Theories
• Boundary conditions for GL-twisted N=4 SYM
• A 5d/2d/4d correspondence
• Conceptual Analysis of Black Hole Entropy in String Theory
• Cobordism invariants from BPS q-series
• Vacuum states of N=1* mass deformations of N=4 and N=2 conformal gauge theories and their brane interpretations
• Cohomological Yang-Mills Theories on Kahler 3-Folds
• M5-branes on S^2 x M_4: Nahm's Equations and 4d Topological Sigma-models
• Elliptic Loci of SU(3) Vacua
• Spurious Poles in the Scattering of Electric and Magnetic Charges
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• On the singular sets of solutions to the Kapustin-Witten equations and the Vafa-Witten ones on compact Kähler surfaces
• Multiple D4-D2-D0 on the Conifold and Wall-crossing with the Flop
• Cutting and gluing with running couplings in $\mathcal{N}=2$ QCD
• U-duality from Matrix Membrane Partition Function
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• Verlinde formulae on complex surfaces: K-theoretic invariants
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• Universal volume of groups and anomaly of Vogel's symmetry
• Torsion and Supersymmetry in Omega-background
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• Cohomological Localization of $\mathcal{N}=2$ Gauge Theories with Matter
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• On the Continuum and Lattice Formulations of N=4 D=3 Twisted Super Yang-Mills
• Gauge theories on compact toric manifolds
• Off-shell structure of twisted (2,0) theory
• Study of gapped phases of 4d gauge theories using temporal gauging of the ${\mathbb{Z}}_N$ 1-form symmetry
• Wilson-'t Hooft operators and the theta angle
• Dual symmetry in a generalized Maxwell theory
• Scaling Black Holes and Modularity
• Geometric Unification of Higgs Bundle Vacua
• Modular Forms as Classification Invariants of 4D N=2 Heterotic--IIA Dual Vacua
• Supersymmetric branes on curved spaces and fluxes
• Five-dimensional topologically twisted maximally supersymmetric Yang-Mills theory
• Some properties of (3+1) dimensional vortex solutions in the extended CP^N Skyrme-Faddeev model
• Gaugino Condensation and Generation of Supersymmetric 3-Form Flux
• Higher dimensional analogue of the Blau-Thompson model and N_T=8, D=2 Hodge-type cohomological gauge theories
• N=4 Supersymmetric Yang-Mills Theory on Orbifold-$T^4/{\mathbf{Z}}_2$
• Matrix Theory, Hilbert Scheme and Integrable System
• A Holographic Kaleidoscope for $\mathcal{N}=1^{\ast }$
• Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality
• Vertical D4-D2-D0 bound states on K3 fibrations and modularity
• The geometry of the M5-branes and TQFTs
• Holomorphic Anomaly in Gauge Theory on ALE space
• Twisted N=4 Super Yang-Mills Theory in Omega-background
• SU(N) transitions in M-theory on Calabi-Yau fourfolds and background fluxes
• The trouble with twisting (2,0) theory
• Noncommutative Instantons in Diverse Dimensions
• On the Supersymmetric Index of the M-theory 5-brane and Little String Theory
• A note on S-duality for the N=1* Sp(2n) and SO(2n+1) super-Yang-Mills theories
• Abelian Projections of the Mass-deformed ABJM theory and Weakly Curved Dual Geometry
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• Dielectric-branes in Non-supersymmetric SO(3)-invariant Perturbation of Three-dimensional N=8 Yang-Mills Theory
• Holographic Renormalization Group Flows: The View from Ten Dimensions
• (0,2) Dualities and the 4-Simplex
• Warped AdS${}_3$, dS${}_3$ and flows from $\mathcal{N}=(0,2)$ SCFTs
• S-duality in Abelian gauge theory revisited
• A lower bound on the solutions of Kapustin-Witten equations
• Minimal Areas from Entangled Matrices
• Topological twisting of conformal supercharges
• Intersecting branes, Higgs sector, and chirality from $\mathcal{N}=4$ SYM with soft SUSY breaking
• Dark energy from topology change induced by microscopic Gauss-Bonnet wormholes
• Entropy of Non-Extreme Rotating Black Holes in String Theories
• New Results on N=4 SuperYang-Mills Theory
• Topological Field Theory and Second-Quantized Five-Branes
• Gravitational free energy in topological AdS/CFT
• Flops and the S-duality conjecture
• Towards Geometric D6-Brane Model Building on non-Factorisable Toroidal ${\mathbb{Z}}_4$-Orbifolds
• Duality and the Legendre Transform
• Comments on chiral algebras and $\Omega$-deformations
• Virtual ${\chi }_{-y}$-genera of Quot schemes on surfaces
• Is Supersymmetric Quantum Mechanics compatible with Duality
• $\widehat{\mathfrak{sl}}(n{)}_N$ WZW conformal blocks from $SU(N)$ instanton partition functions on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• Trialities of minimally supersymmetric 2d gauge theories
• Deformed matrix models, supersymmetric lattice twists and N=1/4 supersymmetry
• Spinning Hopf solitons on S^3 x R
• Matrix models and stochastic growth in Donaldson-Thomas theory
• Mass deformation of twisted super Yang-Mills theory with fuzzy sphere solution
• Pursuing Gravitational S-Duality
• Squashed Toric Manifolds and Higher Depth Mock Modular Forms
• 't Hooft Operators in the Boundary
• BPS states in Matrix Strings
• All supersymmetric solutions of 3D U(1)${}^3$ gauged supergravity
• SL(2,Z) Multiplets in N=4 SYM Theory
• Magnetic Charge Lattices, Moduli Spaces and Fusion Rules
• Lectures on the Microscopic Modeling of the 5-dim. Black Hole of IIB String Theory and the $D_1-D_5$ System
• Self-dual Hopfions
• Cohomological Field Theory Approach to Matrix Strings
• Basic and Equivariant Cohomology in Balanced Topological Field Theory
• Electric-magnetic Duality in Noncommutative Geometry
• S-duality invariant perturbation theory improved by holography
• BPS jumping loci are automorphic
• Monads and D-instantons
• Attractive Strings and Five-Branes, Skew-Holomorphic Jacobi Forms and Moonshine
• A vanishing theorem for T-branes
• N=4 Yang--Mills theory as a complexification of the N=2 theory
• Supersymmetric ground states of 3d $\mathcal{N}=4$ SUSY gauge theories and Heisenberg Algebras
• Mock modularity at work, or black holes in a forest
• Holographic duals of the $\mathcal{N}=1$* gauge theory
• Partition functions of Supersymmetric Gauge Theories in Noncommutative R^{2D} and their Unified Perspective
• Generalised Seiberg-Witten equations and almost-Hermitian geometry
• Four-dimensional topological Einstein-Maxwell gravity
• Topological gauge theories with antisymmetric tensor matter fields
• Radiation Damping of a BPS Monopole; an Implication to S-duality
• Identities for generalized Appell functions and the blow-up formula
• N=4 Instanton Calculus in Omega and R-R Backgrounds
• $n$-th parafermion ${\mathcal{W}}_N$ characters from $U(N)$ instanton counting on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• An Approach to $\mathcal{N}=4$ ADE Gauge Theory on K3
• A Suggestion for Modification of Vafa-Witten Theory
• Refinement and modularity of immortal dyons
• $\mathrm{SU}(r)$ Vafa-Witten invariants, Ramanujan's continued fractions, and cosmic strings
• Three Avatars of Mock Modularity
• Twisted Superalgebras and Cohomologies of the N=2 Superconformal Quantum Mechanics
• The ADHM-like Constructions for Instantons on CP^2 and Three Dimensional Gauge Theories
• On Matrix Models of M5-branes
• Rudiments of Dual Feynman Rules for Yang-Mills Monopoles in Loop Space
• Bulk Witten Indices from D=10 Yang Mills Integrals
• Automorphic properties of (2, 0) theory on T6
• Z(2) monopoles in SU(n) Yang-Mills-Higgs theories
• Branes and DAHA Representations
• Flags of sheaves, quivers and symmetric polynomials
• Vafa-Witten Theory on N=2 and N=4 Twisted Superspace in Four Dimensions
• Astrophysical and cosmological considerations on a string dilaton of a least coupling
• Stable pair invariants on Calabi-Yau threefolds containing P^2
• Low energy limit for the resolvent of some fibered boundary operators
• Global Aspects of Abelian Duality in Dimension Three
• Super Yang-Mills Theories with Inhomogeneous Mass Deformations
• Aspects of Space-Time Dualities
• Cosection localization and the Quot scheme ${\mathrm{Quot}}_S^l(\mathcal{E})$
• Black Hole Entropy Associated with Supersymmetric Sigma Model
• Dilatation Operator and Space-time Geometry
• Secondary products in supersymmetric field theory
• The moduli space of hyper-K{ä}hler four-fold compactifications
• Sigma Models for Bundles on Calabi-Yau: A Proposal for Matrix String Compactifications
• N=4 SYM on K3 and the AdS(3)/CFT(2) Correspondence
• Massless monopole clouds and electric-magnetic duality
• The Covariant Chiral Ring
• A Note on q-Deformed Two-Dimensional Yang-Mills and Open Topological Strings
• Non-Geometric Magnetic Flux and Crossed Modules
• Abelian reductions of deformed $\mathcal{N}=4$ SYM
• Electric-magnetic Duality of Abelian Gauge Theory on the Four-torus, from the Fivebrane on T2 x T4, via their Partition Functions
• Quark confinement via magnetic color-flavor locking
• Lattice Formulation of $\mathcal{N}=2^{\ast }$ Yang-Mills
• N = 4 SYM on Σ\times S^2 and its Topological Reduction
• The Monopole Equations in Topological Yang-Mills
• Boundary Conditions in Topological AdS${}_4$/CFT${}_3$
• Flavor deformations and supersymmetry enhancement in $4d$ $\mathcal{N}=2$ theories
• Topological Yang-Mills Theory with Two Fermionic Charges. A Superfield Approach on Kähler Manifolds
• BPS Z(2) monopoles and N=2 SU(n) superconformal field theories on the Higgs branch
• Four twisted differential operators for the N=4 superconformal algebra
• BPS partition functions in N = 4 Yang-Mills theory on T^4
• Hecke Operator and S-Duality of N=4 Super Yang-Mills for ADE Gauge Group on K3
• Fluctons
• Little Strings, Quasi-topological Sigma Model on Loop Group, and Toroidal Lie Algebras
• Residues and Topological Yang-Mills Theory in Two Dimensions
• Anomalous Currents in SCFT${}_4$
• Non-orientable surfaces and electric-magnetic duality
• Gap Condition and Self-Dualized $\mathcal{N}=4$ Super Yang-Mills Theory for ADE Gauge Group on K3
• Extremal Transitions in Heterotic String Theory
• Higgs Bundles and Four Manifolds
• Rank 2 sheaves on toric 3-folds: classical and virtual counts
• BPS Equations in Omega-deformed N=4 Super Yang-Mills Theory
• Anti-symmetric rank-2 Matter Field on Superspace for N_{T}=2
• S-Duality in N=4 Yang-Mills Theories
• $\mathcal{N}=2^{\ast }$ Yang-Mills on the Lattice
• Duality and Combinatorics of Long Strings in ADS3
• Hilbert schemes, Verma modules and spectral functions of hyperbolic geometry with application to quantum invariants
• The four dimensional Yang--Mills partition function in the vicinity of the vacuum
• New Reflections on Gravitational Duality