Modular Bootstrap of Boundary N = 2 Liouville Theory *

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. Talk presented at strings 2004, June 28-July 2, Paris