Twisted boundary states in Kazama-Suzuki models

TL;DR

This paper constructs and classifies twisted boundary states in Kazama-Suzuki models, revealing automorphism groups larger than charge conjugation and exploring their effects on superconformal symmetry and dualities.

Contribution

It provides explicit forms of twisted Cardy states in Kazama-Suzuki models, including automorphisms beyond charge conjugation, and analyzes their symmetry properties and duality relations.

Findings

Automorphism group contains at least Z_2, often larger.

Explicit twisted Cardy states preserve N=2 superconformal algebra.

Level-rank duality relates different Cardy states and exceptional cases.

Abstract

We construct Cardy states in the Kazama-Suzuki model G/H x U(1), which satisfy the boundary condition twisted by the automorphisms of the coset theory. We classify all the automorphisms of G/H x U(1) induced from those of the G theory. The automorphism group contains at least a Z_2 as a subgroup corresponding to the charge conjugation. We show that in several models there exist extra elements other than the charge conjugation and that the automorphism group can be larger than Z_2. We give the explicit form of the twisted Cardy states which are associated with the non-trivial automorphisms. It is shown that the resulting states preserve the N=2 superconformal algebra. As an illustration of our construction, we give a detailed study for two hermitian symmetric space models SU(4)/SU(2) x SU(2) x U(1) and SO(8)/SO(6) x U(1) both at level one. We also study the action of the level-rank duality on the Cardy states and find the relation with the exceptional Cardy states originated from a conformal embedding.