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.
Cite
@article{arxiv.1011.3798,
title = {Elliptic beta integrals and solvable models of statistical mechanics},
author = {V. P. Spiridonov},
journal= {arXiv preprint arXiv:1011.3798},
year = {2012}
}
Comments
30 pp., version to appear in Contemp. Math