Super Liouville Theory with Boundary

TL;DR

This paper explores N=1 super Liouville theory on worldsheets with boundaries, classifying boundary states, analyzing correlation functions, and examining boundary operators, revealing differences from bosonic cases.

Contribution

It provides a classification of boundary states using modular properties and investigates boundary operators and their connections in super Liouville theory.

Findings

Boundary states classified via modular transformations.

Two distinct boundary conditions lead to different boundary states.

Boundary degenerate operators connect boundary states in complex ways.

Abstract

We study N=1 super Liouville theory on worldsheets with and without boundary. Some basic correlation functions on a sphere or a disc are obtained using the properties of degenerate representations of superconformal algebra. Boundary states are classified by using the modular transformation property of annulus partition functions, but there are some of those whose wave functions cannot be obtained from the analysis of modular property. There are two ways of putting boundary condition on supercurrent, and it turns out that the two choices lead to different boundary states in quality. Some properties of boundary vertex operators are also presented. The boundary degenerate operators are shown to connect two boundary states in a way slightly complicated than the bosonic case.