Wrapping rules (in) string theory

TL;DR

This paper introduces universal wrapping rules to determine the count of 1/2-BPS branes in string theory compactifications, including exotic and lower-supersymmetry cases, providing a unified framework for brane enumeration.

Contribution

It formulates universal wrapping rules applicable to all 1/2-BPS branes, including exotic branes and those in reduced supersymmetry scenarios, extending previous understanding.

Findings

Wrapping rules accurately count 1/2-BPS branes in various compactifications.

Rules incorporate an additional combinatorial factor for exotic branes.

Application demonstrated on IIA/IIB compactification on specific orbifolds.

Abstract

In this paper we show that the number of all 1/2-BPS branes in string theory compactified on a torus can be derived by universal wrapping rules whose formulation we present. These rules even apply to branes in less than ten dimensions whose ten-dimensional origin is an exotic brane. In that case the wrapping rules contain an additional combinatorial factor that is related to the highest dimension in which the ten-dimensional exotic brane, after compactification, can be realized as a standard brane. We show that the wrapping rules also apply to cases with less supersymmetry. As a specific example, we discuss the compactification of IIA/IIB string theory on $(T^4/{\mathbb{Z}_2}) \times T^n$.