Relevant Perturbations of the SU(1,1)/U(1) Coset

TL;DR

This paper investigates relevant perturbations in the $SU(1,1)/U(1)$ coset model, showing how certain relevant operators induce a flow to the $SU(2)/U(1)$ model, linking black hole and spherical geometries.

Contribution

It identifies a class of relevant operators forming a closed fusion algebra that enable renormalizable perturbations of the coset model and describes the resulting renormalization group flow.

Findings

Relevant operators form a closed fusion algebra.

Perturbations lead to a flow from the black hole to spherical geometry.

The IR fixed point corresponds to the $SU(2)/U(1)$ coset at positive level.

Abstract

It is shown that the space of cohomology classes of the $SU(1,1)/U(1)$ coset at negative level $k$ contains states of relevant conformal dimensions. These states correspond to the energy density operator of the associated nonlinear sigma model. We exhibit that there exists a subclass of relevant operators forming a closed fusion algebra. We make use of these operators to perform renormalizable perturbations of the $SU(1,1)/U(1)$ coset. In the infra-red limit, the perturbed theory flows to another conformal model. We identify one of the perturbative conformal points with the $SU(2)/U(1)$ coset at positive level. {}From the point of view of the string target space geometry, the given renormalization group flow maps the euclidean black hole geometry described by the $SU(1,1)/U(1)$ coset into the sphere described by the $SU(2)/U(1)$ coset.