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

TL;DR

This paper provides a comprehensive analysis of D-branes in the SL(2,R)/U(1) coset conformal field theory, introducing new D2-brane configurations and verifying their consistency with established boundary state conditions.

Contribution

It introduces a new class of D2-branes in the SL(2,R)/U(1) model and applies the modular bootstrap approach with extended characters and algebra embeddings.

Findings

D0- and D1-branes match previous results

D2-branes are a novel class with specific geometric properties

Boundary states satisfy Cardy conditions

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.