Towards a supersymmetric classification of D-brane configurations with odd spin structure

TL;DR

This paper develops a framework for classifying D-brane configurations with odd spin structures using supersymmetry conditions and mathematical identities, highlighting the importance of RR zero mode regularization.

Contribution

It introduces a supersymmetric classification scheme for D-branes with odd spin structures based on Riemann Theta identities and integer matrix conditions.

Findings

Mapped supersymmetry preservation to integer matrix equations

Highlighted the role of RR zero mode regularization

Provided a classification approach for D-brane configurations

Abstract

We consider the construction of a general tree level amplitude for the interactions between dynamical D-branes where the configurations have non-zero odd spin structure. Using Riemann Theta Identities we map the conditions for the preservation of some supersymmetry to a set of integer matrices satisfying a simple but non-trivial equation. We also show how the regularization of the RR zero modes plays an important role in determining which configurations are permitted.