Elliptic beta integrals and solvable models of statistical mechanics

Details Elliptic beta integrals and solvable models of statistical mechanics Elliptic beta integrals and solvable models of statistical mechanics

2010-11-16

arxiv.org/abs/1011.3798v2

Physics

High Energy Physics

High Energy Physics - Theory

30 pp., version to appear in Contemp. Math

Scientific paper

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.

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