Gepner-like boundary states on $T^4$

TL;DR

This paper constructs exact boundary states for D-branes in type II superstring theory on self-dual 4-tori, revealing stable and unstable configurations, including known BPS states and new non-BPS branes, using a Gepner-like approach.

Contribution

It introduces a novel Gepner-like method to describe D-branes on $T^4$ with boundary states not constrained by free-field gluing conditions.

Findings

Derived explicit boundary states for various D-branes on $T^4$.

Identified stable BPS and non-BPS D-branes, including new non-RR charged states.

Demonstrated the effectiveness of permutation gluing conditions in classifying D-branes.

Abstract

We present exact expressions for elementary boundary states which describe D-branes preserving 16 or fewer supercharges in type II superstring compactified on certain self-dual 4-tori. While being manifestly superconformal, our boundary states are not a priori required to satisfy the usual free-field gluing conditions along the internal directions of the 4-tori. Our calculations proceed along the lines of Gepner's construction by recasting the $\mathcal{N}=(2,2)$ worldsheet sigma model on the 4-tori in terms of $\mathcal{N}=2$ minimal models. Imposing general permutation gluing conditions on the $\mathcal{N}=(2,2)$ generators is shown to yield various stable and unstable D-branes, where the stable ones include the known 1/2-BPS and 1/4-BPS bound states of D$p$-branes, as well as new non-BPS D-branes, which do not carry RR charges.