Solution of the H3+ model on a disc

TL;DR

This paper explicitly solves the correlators of the H3+ model on a disc with AdS2-brane boundary conditions by relating them to Liouville theory correlators, revealing unique features of boundary states and symmetries.

Contribution

It provides a complete solution for the H3+ model on a disc with AdS2-branes, connecting it to Liouville theory and analyzing boundary correlators and symmetries.

Findings

Correlators of the H3+ model are expressed in terms of Liouville theory correlators.

Cardy-Lewellen constraints are weaker but still sufficient for certain correlators.

Open string states between different AdS2-branes belong to the universal covering group of SL(2,R).

Abstract

We determine all the correlators of the H3+ model on a disc with AdS2-brane boundary conditions in terms of correlators of Liouville theory on a disc with FZZT-brane boundary conditions. We argue that the Cardy-Lewellen constraints are weaker in the H3+ model than in rational conformal field theories due to extra singularities of the correlators, but strong enough to uniquely determine the bulk two-point function on a disc. We confirm our results by detailed analyses of the bulk-boundary two-point function and of the boundary two-point function. In particular we find that, although the target space symmetry preserved by AdS2-branes is the group SL(2,R), the open string states between two distinct parallel AdS2-branes belong to representations of the universal covering group.