Elliptic beta integrals and solvable models of statistical mechanics

Nov, 2010
24 pages
Published in:
  • Contemp.Math. 563 (2012) 181-211
e-Print:

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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