Exact One-Point Function of N=1 super-Liouville Theory with Boundary

TL;DR

This paper derives exact one-point functions for N=1 super-Liouville theory with boundaries, connecting them to boundary conditions, superconformal symmetry, and modular properties, advancing understanding of boundary CFTs.

Contribution

It provides the first exact one-point functions for N=1 super-Liouville theory with boundaries, including on pseudosphere and with explicit boundary actions, and relates these to Cardy conditions and modular matrices.

Findings

Exact one-point functions on pseudosphere and with boundary actions.

Relation of one-point functions to generalized Cardy conditions.

Conjecture on boundary two-point functions dependence.

Abstract

In this paper, exact one-point functions of N=1 super-Liouville field theory in two-dimensional space-time with appropriate boundary conditions are presented. Exact results are derived both for the theory defined on a pseudosphere with discrete (NS) boundary conditions and for the theory with explicit boundary actions which preserves super conformal symmetries. We provide various consistency checks. We also show that these one-point functions can be related to a generalized Cardy conditions along with corresponding modular $S$-matrices. Using this result, we conjecture the dependence of the boundary two-point functions of the (NS) boundary operators on the boundary parameter.