D-branes in Kazama-Suzuki Models

TL;DR

This work analyzes D-branes in Kazama--Suzuki coset backgrounds, showing that D-brane geometry realizes a generalised calibration in the presence of a nonzero $B$-field. It derives boundary conditions for KS boundary states, identifying A-type (lagrangian) and B-type (complex) supersymmetric cycles in $G/H$, and explains how these cycles are locally calibrated yet not necessarily globally minimal. The review of supersymmetric cycles highlights the role of the $(2,2)$ SCA and the ferent integrability constraints, with Hermitian symmetric cases recovering true calibration. Abelian T-duality is then shown to act via Weyl transformations, mapping A- and B-type cycles (and the IIA/IIB theories) in a dimension-dependent fashion, reflecting the underlying gauged WZW structure and the coset geometry.

Abstract

We investigate boundary states of D-branes wrapped around supersymmetric cycles in Kazama--Suzuki models. We show that the geometry of the D-branes corresponds to a generalisation of calibrated geometry. We comment on the link with the geometry of the coset space and discuss how T-duality maps between these boundary states.