The conformal boundary states for SU(2) at level 1

TL;DR

This paper classifies conformal boundary states in the SU(2) WZW model at level one, showing they are parametrized by SL(2,C) group elements, extending the understanding of boundary conditions in conformal field theory.

Contribution

It determines the most general conformal boundary states for SU(2) level one, including their parametrization by SL(2,C), under the assumption of consistency of Cardy states and deformations.

Findings

Boundary states are parametrized by SL(2,C) group elements.

Most general conformal boundary states are identified.

Assumption of Cardy state consistency guides the classification.

Abstract

For the case of the SU(2) WZW model at level one, the boundary states that only preserve the conformal symmetry are analysed. Under the assumption that the usual Cardy boundary states as well as their marginal deformations are consistent, the most general conformal boundary states are determined. They are found to be parametrised by group elements in SL(2,C).