Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices

Abstract

We consider Seiberg electric-magnetic dualities for 4d $\mathcal{N}=1$ SYM theories with SO(N) gauge group. For all such known theories we construct superconformal indices (SCIs) in terms of elliptic hypergeometric integrals. Equalities of these indices for dual theories lead both to proven earlier special function identities and new conjectural relations for integrals. In particular, we describe a number of new elliptic beta integrals associated with the s-confining theories with the spinor matter fields. Reductions of some dualities from SP(2N) to SO(2N) or SO(2N+1) gauge groups are described. Interrelation of SCIs and the Witten anomaly is briefly discussed. Possible applications of the elliptic hypergeometric integrals to a two-parameter deformation of 2d conformal field theory and related matrix models are indicated. Connections of the reduced SCIs with the state integrals of the knot theory, generalized AGT duality for (3+3)d theories, and a 2d vortex partition function are described.

Latex, 58 pages; paper shortened, to appear in Commun. Math. Phys

References in corpus (44)

• Rigid Supersymmetric Theories in Curved Superspace
• SUSY Gauge Theories on Squashed Three-Spheres
• Notes on SUSY Gauge Theories on Three-Sphere
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Counting Gauge Invariants: the Plethystic Program
• Seiberg Duality in Chern-Simons Theory
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• Knot Invariants from Four-Dimensional Gauge Theory
• From 4d superconformal indices to 3d partition functions
• Generalized Superconformal Index for Three Dimensional Field Theories
• Supersymmetry enhancement by monopole operators
• Essays on the theory of elliptic hypergeometric functions
• Relation between the 4d superconformal index and the S^3 partition function
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
• Superconformal indices for N=1 theories with multiple duals
• Calculating the Superconformal Index and Seiberg Duality
• Counting BPS operators in N=4 SYM
• Vertices, Vortices & Interacting Surface Operators
• 3D-partition functions on the sphere: exact evaluation and mirror symmetry
• AGT on the S-duality Wall
• N=4 Superconformal Characters and Partition Functions
• Reducing the 4d Index to the S^3 Partition Function
• Notes on Ding-Iohara algebra and AGT conjecture
• Elliptic hypergeometric integrals and 't Hooft anomaly matching conditions
• Properties of generalized univariate hypergeometric functions
• New and old N=8 superconformal field theories in three dimensions
• Seiberg-like duality in three dimensions for orthogonal gauge groups
• Semiclassical Analysis of the 3d/3d Relation
• The Liouville side of the Vortex
• On the ISS model of dynamical SUSY breaking
• Non-Abelian Confinement in N=2 Supersymmetric QCD: Duality and Kinks on Confining Strings
• Index for Supergravity on AdS_5 \times T^{1,1} and Conifold Gauge Theory
• Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index
• Supersymmetric dualities beyond the conformal window
• Quantum Riemann Surfaces in Chern-Simons Theory
• Chern-Simons Theory and S-duality
• 4D and 2D superconformal index with surface operator
• Localization of Vortex Partition Functions in $\mathcal{N}=(2,2)$ Super Yang-Mills theory
• Finite N Index and Angular Momentum Bound from Gravity
• Duality In Two-Dimensional (2,2) Supersymmetric Non-Abelian Gauge Theories
• New dynamics and dualities in supersymmetric chiral gauge theories

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• Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs
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• Dualities from dualities: the sequential deconfinement technique
• The $SL(2,\mathbb{Z})$ dualization algorithm at work
• Superconformal indices and partition functions for supersymmetric field theories
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• Index for Three Dimensional Superconformal Field Theories and Its Applications
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• On Bailey pairs for $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$
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