Wound D-branes in Gepner Models

TL;DR

This paper introduces a new method for representing D-branes in Gepner models using a projection on boundary states, enabling the description of more general homology classes while preserving supersymmetry.

Contribution

It proposes a novel prescription for D-brane boundary states in Gepner models, extending their homology class representation beyond previous methods.

Findings

Boundary states preserve spacetime supersymmetry.

Constructed boundary states for D-branes on arbitrary 1-cycles.

Angle-dependent transformations are essential for correct intersection numbers.

Abstract

We propose a new prescription of how to represent D-branes in Gepner models in more general homology classes than those in the previous constructions. The central role is played by a certain projection acting on the Recknagel-Schomerus boundary states. Consequently, the boundary states are in most cases no longer a sum of products of N=2 Ishibashi states, but nevertheless preserve spacetime supersymmetry and satisfy the Cardy condition. We demonstrate these in the (k=1)^3 Gepner model in detail, and construct boundary states for D-branes wound around arbitrary rigid 1-cycles on the corresponding 2-torus. We also emphasize the necessity of some angle-dependent transformations in identifying a proper free-field realization for each brane tilted at an angle. In particular, this is essential for the Witten index to give the correct intersection numbers between the different D-branes.