On Bailey pairs for $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$

Abstract

We study Bailey pairs construction for hyperbolic hypergeometric integral identities acquired via the duality of lens partitions functions for the three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$. The novel Bailey pairs are constructed for the star-triangle relation, the star-star relation and the pentagon identity. The first two of them are integrability conditions for the Ising-type integrable lattice models. The last one corresponds to the representation of the basic $2-3$ Pachner move for triangulated 3-manifolds.

arXiv comment26 pages, v2: minor corrections, v3: minor corrections and comments added

References in corpus (60)

• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Mirror Symmetry in Three Dimensional Gauge Theories
• SUSY Gauge Theories on Squashed Three-Spheres
• Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
• Discrete Heisenberg-Weyl Group and Modular Group
• Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U_q(sl(2,R))
• Nonperturbative Tests of Three-Dimensional Dualities
• Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality
• 4d Index to 3d Index and 2d TQFT
• From 4d superconformal indices to 3d partition functions
• Elliptic hypergeometry of supersymmetric dualities
• Essays on the theory of elliptic hypergeometric functions
• Unitary representations of $U_{q}(\mathfrak{sl}(2,\RR))$, the modular double, and the multiparticle q-deformed Toda chains
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Noncommutative Hypergeometry
• 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
• Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
• An E7 Surprise
• Factorisation and holomorphic blocks in 4d
• The large N limit of M2-branes on Lens spaces
• S^3/Z_n partition function and dualities
• Quivers, YBE and 3-manifolds
• Elliptic gamma-function and multi-spin solutions of the Yang-Baxter equation
• Exact solution of the Faddeev-Volkov model
• From Quantum Groups to Liouville and Dilaton Quantum Gravity
• Chern-Simons theory on L(p,q) lens spaces and Localization
• Factorization of S^3/Z_n partition function
• New solutions of the star-triangle relation with discrete and continuous spin variables
• A Bailey tree for integrals
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• The star-triangle relation and 3d superconformal indices
• Hyperbolic Structure Arising from a Knot Invariant
• How to resum perturbative series in 3d N=2 Chern-Simons matter theories
• Quiver gauge theories and integrable lattice models
• A new pentagon identity for the tetrahedron index
• $q$-Virasoro modular double and 3d partition functions
• Comment on star-star relations in statistical mechanics and elliptic gamma-function identities
• Integrability from 2d N=(2,2) Dualities
• On the solutions of the Yang-Baxter equations with general inhomogeneous eight-vertex $R$-matrix: Relations with Zamolodchikov's tetrahedral algebra
• Basic hypergeometry of supersymmetric dualities
• A Higher-level Bailey Lemma
• Self-dual Continuous Series of Representations for U_q(sl(2)) and U_q(osp(1|2))
• Superconformal indices and partition functions for supersymmetric field theories
• A Trinomial Analogue of Bailey's Lemma and N=2 Superconformal Invariance
• Orthogonal Polynomials in Mathematical Physics
• Integrable lattice spin models from supersymmetric dualities
• Mathematical structures behind supersymmetric dualities
• From rarefied elliptic beta integral to parafermionic star-triangle relation
• Star-triangle type relations from $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$ dualities
• Lens partition function, pentagon identity and star-triangle relation
• The rarefied elliptic Bailey lemma and the Yang-Baxter equation
• On beta pentagon relations
• New solutions to the $s{\ell }_q(2)$-invariant Yang-Baxter equations at roots of unity: cyclic representations
• Hyperbolic and trigonometric hypergeometric solutions to the star-star equation
• New Pentagon Identities Revisited
• Superconformal indices, Seiberg dualities and special functions
• 4d $\mathcal{N}=1$ quiver gauge theories and the ${\mathrm{A}}_{\mathrm{n}}$ Bailey lemma
• Rational hypergeometric identities