The GL(1|1)-symplectic fermion correspondence

TL;DR

This paper establishes a correspondence between the GL(1|1) WZNW model and a free theory with scalars and symplectic fermions, providing new insights into boundary states and string amplitudes in this context.

Contribution

It proves a new correspondence between the GL(1|1) WZNW model and a free scalar-symplectic fermion model, including detailed boundary state analysis and string amplitude computations.

Findings

Correlation functions match known results for scalars and symplectic fermions.

Boundary states for symplectic fermions are explicitly constructed.

New string amplitudes between different brane types are computed and satisfy Cardy's condition.

Abstract

In this note we prove a correspondence between the Wess-Zumino-Novikov-Witten model of the Lie supergroup GL(1|1) and a free model consisting of two scalars and a pair of symplectic fermions. This model was discussed earlier by LeClair. Vertex operators for the symplectic fermions include twist fields, and correlation functions of GL(1|1) agree with the known results for the scalars and symplectic fermions. We perform a detailed study of boundary states for symplectic fermions and apply them to branes in GL(1|1). This allows us to compute new amplitudes of strings stretching between branes of different types and confirming Cardy's condition.