D-branes in N=2 Liouville and its mirror

TL;DR

The paper analyzes D-branes in the mirror pair of $N=2$ Liouville and the supersymmetric $SL(2,\mathbb{R})/U(1)$ coset, constructing D0, D1, and D2 branes via boundary state methods and exploring their holographic relevance. It clarifies the bulk spectrum, the duality between the coset and Liouville theories, and employs conformal bootstrap ideas to frame boundary data, including decoupling of bulk and localized poles in one-point functions. Explicit Cardy checks are carried out for D0 and D1 branes, with a careful orbifold extension ($\mathbb{Z}_p$) and a detailed analysis of their open/closed string channel relations; D2-branes are analyzed but exhibit subtleties requiring further interpretation. Overall, the work advances concrete boundary CFT constructions in non-compact $N=2$ backgrounds, illuminating boundary-state data, dualities, and potential holographic applications to Little String Theory.

Abstract

We study D-branes in the mirror pair N=2 Liouville / supersymmetric SL(2,R)/U(1) coset superconformal field theories. After revisiting the duality between the two models, we build D0, D1 and D2 branes, on the basis of the boundary state construction for the Euclidean AdS(3) conformal field theory. We also construct D0-branes in an orbifold that rotates the angular direction of the cigar. We show how the poles of correlators associated to localized states and bulk interactions naturally decouple in the one-point functions of localized and extended branes. We stress the role played in the analysis of D-brane spectra by primaries in SL(2,R)/U(1) which are descendents of the parent theory.

Figures (2)

• Figure 1: Choice of contour of integration (for $\tau_1>0$).
• Figure 2: Change of contour of integration (case $w>\frac{k \nu_2}{2}$).