Counting minimal form factors of the restricted sine-Gordon model

Abstract

We revisit the issue of counting all local fields of the restricted sine-Gordon model, in the case corresponding to a perturbation of minimal unitary conformal field theory. The problem amounts to the study of a quotient of certain space of polynomials which enter the integral representation for form factors. This space may be viewed as a $q$-analog of the space of conformal coinvariants associated with U_q(sl_{2}^) with q=\sqrt{-1}. We prove that its character is given by the restricted Kostka polynomial multiplied by a simple factor. As a result, we obtain a formula for the truncated character of the total space of local fields in terms of the Virasoro characters.

58 pages, final version, Proposition 2.8 modified

Cited by in corpus (2)

• The Space of Local Fields as a Module over the Ring of Local Integrals of Motion
• A functional model for the tensor product of level 1 highest and level -1 lowest modules for the quantum affine algebra U_q(sl_{2}^)