Aspects of WZW models at critical level

TL;DR

This paper investigates non-compact WZW models at critical level as tensionless string limits, focusing on the Euclidean black hole coset, revealing symmetry truncations and dualities, but leaving some physical interpretations unresolved.

Contribution

It introduces the analysis of WZW models at critical level as tensionless limits and explores their symmetry structures and dualities, especially for the Euclidean black hole coset.

Findings

Gravity decouples as a Liouville field with infinite background charge.

World-sheet symmetry reduces to a truncated W_infinity without Virasoro.

Langlands duality relates small and large level regimes.

Abstract

We consider non-compact WZW models at critical level (equal to the dual Coxeter number) as tensionless limits of gravitational backgrounds in string theory. Special emphasis is placed on the Euclidean black hole coset SL(2,R)_k/U(1) when k=2. In this limit gravity decouples in the form of a Liouville field with infinite background charge and the world-sheet symmetry of the model becomes a truncated version of W_\infty without Virasoro generator. This is regarded as manifestation of Langlands duality for the SL(2,R)_k current algebra that relates small with large values of the level in the two extreme limits. However, the physical interpretation of the SL(2,R)_k/U(1) coset model below the self-dual value k=3 remains elusive including the non-conformal theory at k=2.