Modular bootstrap of boundary [formula omitted] 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 ) super-coset 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. To cite this article: T. Eguchi, C. R. Physique 6 (2005).