Abstract
We present a detailed study of D-branes in the axially gauged SL ( 2 , R ) k / 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 AdS 3 model). The D2-branes are new. They are not, in general, space-filling but extend from the asymptotic circle at infinity up to a minimum distance ρ min ⩾ 0 from the tip of the cigar.
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