N=2 Liouville Theory with Boundary

TL;DR

This paper analyzes N=2 Liouville theory with boundaries, deriving boundary states, interactions, and open string spectra, advancing understanding of boundary phenomena in this supersymmetric conformal field theory.

Contribution

It introduces a comprehensive approach to boundary states in N=2 Liouville theory, combining modular bootstrap and boundary operator methods, and proposes explicit boundary interactions.

Findings

Derived structure constants for the theory.

Constructed boundary states from two different approaches.

Validated boundary interactions through consistency checks.

Abstract

We study N=2 Liouville theory with arbitrary central charge in the presence of boundaries. After reviewing the theory on the sphere and deriving some important structure constants, we investigate the boundary states of the theory from two approaches, one using the modular transformation property of annulus amplitudes and the other using the bootstrap of disc two-point functions containing degenerate bulk operators. The boundary interactions describing the boundary states are also proposed, based on which the precise correspondence between boundary states and boundary interactions is obtained. The open string spectrum between D-branes is studied from the modular bootstrap approach and also from the reflection relation of boundary operators, providing a consistency check for the proposal.