Modular Bootstrap of Boundary N=2 Liouville Theory

TL;DR

This paper develops a modular bootstrap approach to boundary N=2 Liouville theory, deriving boundary states and comparing them with dual supercoset models, revealing consistent results and insights into dualities.

Contribution

It introduces a modular bootstrap method to classify boundary states in N=2 Liouville theory and compares these with supercoset models, advancing understanding of boundary dynamics and dualities.

Findings

Derived three classes of boundary states for N=2 Liouville theory.

Found agreement with semi-classical results from supercoset models.

Provided insights into duality and boundary dynamics in N=2 Liouville theory.

Abstract

We present our recent studies on the dynamics of boundary N=2 Liouville theory. We use the representation theory of N=2 superconformal algebra and the method of modular bootstrap to derive three classes of boundary states of the N=2 Liouville theory. Class 1 and 2 branes are analogues of ZZ and FZZT branes of N=0,1 Liouville theory while class 3 branes come from U(1) degrees of freedom. We compare our results with those of SL(2;R)/U(1) supercoset which is known to be T-dual to N=2 Liouville theory and describes the geometry of 2d black hole. We find good agreements with known results in SL(2;R)/U(1) theory obtained by semi-classical analysis using DBI action. We also comment on the duality of N=2 Liouville theory.