Elliptic beta integrals and solvable models of statistical mechanics
Nov, 2010Citations per year
Abstract: (arXiv)
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.Note:
- 30 pp., version to appear in Contemp. Math
- field theory: conformal
- model: integrability
- duality: transformation
- supersymmetry: duality
- field theory: topological
- gauge field theory: quiver
- Yang-Baxter equation
- statistical mechanics
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