Scaling Lee-Yang model on a sphere 1. Partition function

Abstract

Some general properties of perturbed (rational) CFT in the background metric of symmetric 2D sphere of radius R are discussed, including conformal perturbation theory for the partition function and the large R asymptotic. The truncated conformal space scheme is adapted to treat numerically perturbed rational CFT's in the spherical background. Numerical results obtained for the scaling Lee-Yang model lead to the conclusion that the partition function is an entire function of the coupling constant. Exploiting this analytic structure we are able to describe, starting only with the CFT information and few first terms of conformal perturbation theory, rather precisely the "experimental" truncated space data, including even the large R behavior. © SISSA/ISAS 2002.