On the tensionless limit of gauged WZW models

TL;DR

This paper investigates the tensionless limit of gauged WZW models at critical level, revealing decoupling of gravity, emergence of higher spin symmetries, and geometric and conformal invariance breakdown, with implications for target space and world-sheet theories.

Contribution

It provides a detailed analysis of the tensionless limit, showing how gravity decouples and higher spin symmetries emerge, and explores the geometric and conformal structure changes in this limit.

Findings

Gravity decouples from the spectrum at critical level.

Higher spin symmetries form a truncated W_{} algebra.

Target space geometry becomes an infinitely curved hyperboloid.

Abstract

The tensionless limit of gauged WZW models arises when the level of the underlying Kac-Moody algebra assumes its critical value, equal to the dual Coxeter number, in which case the central charge of the Virasoro algebra becomes infinite. We examine this limit from the world-sheet and target space viewpoint and show that gravity decouples naturally from the spectrum. Using the two-dimensional black-hole coset SL(2,R)_k/U(1) as illustrative example, we find for k=2 that the world-sheet symmetry is described by a truncated version of W_{\infty} generated by chiral fields with integer spin s \geq 3, whereas the Virasoro algebra becomes abelian and it can be consistently factored out. The geometry of target space looks like an infinitely curved hyperboloid, which invalidates the effective field theory description and conformal invariance can no longer be used to yield reliable space-time interpretation. We also compare our results with the null gauging of WZW models, which correspond to infinite boost in target space and they describe the Liouville mode that decouples in the tensionless limit. A formal BRST analysis of the world-sheet symmetry suggests that the central charge of all higher spin generators should be fixed to a critical value, which is not seen by the contracted Virasoro symmetry. Generalizations to higher dimensional coset models are also briefly discussed in the tensionless limit, where similar observations are made.