This article is cited in 7 papers

Matching branches of a nonperturbative conformal block at its singularity divisor

H. Itoyama^ab, A. D. Mironov^cde, A. Yu. Morozov<sup>de

a</sup> Osaka City University Advanced Mathematical Institute (OCAMI), Osaka, Japan
^b Department of Mathematics and Physics, Osaka City University, Osaka, Japan
^c Lebedev Physical Institute, Moscow, Russia
^d Institute for Experimental and Theoretical Physics, Moscow, Russia
^e National Research Nuclear University MEPhI, Moscow, Russia

Abstract: A conformal block is a function of many variables, usually represented as a formal series with coefficients that are certain matrix elements in the chiral {(}i.e., Virasoro{\rm)} algebra. A nonperturbative conformal block is a multivalued function defined globally over the space of dimensions and has many branches and, perhaps, additional free parameters not seen at the perturbative level. We discuss additional complications of the nonperturbative description that arise because all the best-studied examples of conformal blocks are at the singularity locus in the moduli space {\rm(}at divisors of the coefficients or, simply, at zeros of the Kac determinant{\rm).} A typical example is the Ashkin–Teller point, where at least two naive nonperturbative expressions are provided by the elliptic Dotsenko–Fateev integral and by the celebrated Zamolodchikov formula in terms of theta constants, and they differ. The situation is somewhat similar at the Ising and other minimal model points.

Keywords: two-dimensional conformal theory, conformal block.

Received: 20.01.2015

DOI: 10.4213/tmf8856

 English version: Theoretical and Mathematical Physics, 2015, 184:1, 891–923

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