Projections in string theory and boundary states for Gepner models

TL;DR

This work examines how supersymmetry-projections in string theory interact with open-string boundaries, focusing on Gepner-model compactifications equipped with Calabi–Yau extensions. By employing simple-current extensions, the bosonic-string map, and quantum Galois theory, the authors construct and classify A-type boundary states that preserve the extended chiral algebra and at least one space-time SUSY, including fixed-point resolution and automorphism-type distinctions. They provide explicit boundary-state constructions for Gepner models, derive the associated annulus coefficients as CY fusion-structure constants, and analyze the role of A$_0$-type boundaries as a Cardy-accessible subset, while also discussing B-type boundaries via mirror symmetry and obstructions to lifting automorphisms. The paper clarifies the model-independent nature of annulus-integrality, connects world-sheet to space-time SUSY in a boundary-context, and discusses the relationship between Gepner fixed points and geometric singularities, highlighting open problems in brane physics on Calabi–Yau manifolds.

Abstract

In string theory various projections have to be imposed to ensure supersymmetry. We study the consequences of these projections in the presence of world sheet boundaries. A-type boundary conditions come in several classes; only boundary fields that do not change the class preserve supersymmetry. Our analysis takes in particular properly into account the resolution of fixed points under the projections. Thus e.g. the compositeness of some previously considered boundary states of Gepner models follows from chiral properties of the projections. Our arguments are model independent; in particular, integrality of all annulus coefficients is ensured by model independent arguments.