Elliptic beta integrals and solvable models of statistical mechanics

Abstract

The univariate elliptic beta integral was discovered by the author in 2000. Recently Bazhanov and Sergeev have interpreted it as a star-triangle relation (STR). This important observation is discussed in more detail in connection to author's previous work on the elliptic modular double and supersymmetric dualities. We describe also a new Faddeev-Volkov type solution of STR, connections with the star-star relation, and higher-dimensional analogues of such relations. In this picture, Seiberg dualities are described by symmetries of the elliptic hypergeometric integrals (interpreted as superconformal indices) which, in turn, represent STR and Kramers-Wannier type duality transformations for elementary partition functions in solvable models of statistical mechanics.

30 pp., version to appear in Contemp. Math

References in corpus (9)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• S-duality and 2d Topological QFT
• R-Twisting and 4d/2d Correspondences
• Essays on the theory of elliptic hypergeometric functions
• Superconformal indices for N=1 theories with multiple duals
• Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
• Exact solution of the Faddeev-Volkov model
• Superconformal indices of $\mathcal{N}=4$ SYM field theories
• Supersymmetric dualities beyond the conformal window

Cited by in corpus (17)

• From 4d superconformal indices to 3d partition functions
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Elliptic gamma-function and multi-spin solutions of the Yang-Baxter equation
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• Surface defects and elliptic quantum groups
• Elliptic hypergeometric sum/integral transformations and supersymmetric lens index
• A new pentagon identity for the tetrahedron index
• Comment on star-star relations in statistical mechanics and elliptic gamma-function identities
• Integrability from 2d N=(2,2) Dualities
• The Endless Beta Integrals
• Integrable quad equations derived from the quantum Yang-Baxter equation
• A duality web of linear quivers
• Intertwining operators for Sklyanin algebra and elliptic hypergeometric series
• Branes and integrable lattice models
• A New Integrable Ising-type Model from 2d $\mathcal{N}$=(2,2) Dualities
• Pentagon identities arising in supersymmetric gauge theory computations
• Aspects of elliptic hypergeometric functions