D-branes and extended characters in SL(2,R)/U(1)

Abstract

We present a detailed study of D-branes in the axially gauged SL(2,R)/U(1) coset conformal field theory for integer level k. Our analysis is based on the modular bootstrap approach and utilizes the extended SL(2,R)/U(1) characters and the embedding of the parafermionic coset algebra in the N=2 superconformal algebra. We propose three basic classes of boundary states corresponding to D0-, D1- and D2-branes. We verify that these boundary states satisfy the Cardy consistency conditions and discuss their physical properties. The D0- and D1-branes agree with those found in earlier work by Ribault and Schomerus using different methods (descent from the Euclidean AdS3 model). The D2-branes are new. They are not, in general, space-filling but extend from the asymptotic circle at infinity up to a circular boundary at some distance from the tip of the cigar.Comment: 61 pages, 1 figure, 1 table; v2 typos corrected, added a subsection with comments on B-type class 3 boundary states; v3 more typos corrected, version to appear in NP