  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.
