Zamolodchikov operator-valued relations for SL(2,R)_k WZNW model

TL;DR

This paper derives an infinite set of operator-valued relations for reducible representations of the sl(2)_k algebra, analogous to Zamolodchikov's relations in Liouville theory, with potential implications for AdS_3/CFT_2 correspondence.

Contribution

It introduces new operator-valued relations for the sl(2)_k algebra, expanding understanding of its reducible representations and their role in boundary theories.

Findings

Derived infinite operator-valued relations for sl(2)_k

Relations are analogous to Zamolodchikov's in Liouville theory

Potential relevance for AdS_3/CFT_2 boundary correspondence

Abstract

An infinite set of operator-valued relations that hold for reducible representations of the sl(2)_k algebra is derived. These relations are analogous to those recently obtained by Zamolodchikov which involve logarithmic fields associated to the Virasoro degenerate representations in Liouville theory. The fusion rules of the sl(2)_k algebra turn out to be a crucial step in the analysis. The possible relevance of these relations for the boundary theory in the AdS_3/CFT_2 correspondence is suggested.