Wrapping rules (in) string theory

Eric A Bergshoeff,Fabio Riccioni

doi:10.1007/jhep01(2018)046

Eric A Bergshoeff, Fabio Riccioni

Open Access

https://doi.org/10.1007/jhep01(2018)046

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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 (T4/ℤ2) × Tn.

Highlights

G of the corresponding (D − 2), (D − 1) and D-form potentials, resprectively
We extended these rules to a set of generalized wrapping rules that are even valid for families of branes that are not related, via duality, to any brane with a 10D brane origin
The generalization consists of the fact that the number of branes produced by the basic wrapping rules (1.2) and (1.3) must be multiplied by an additional combinatorial factor that is determined by the mixed-index structure of the 10D potential that gives rise to the highest-dimensional brane in the family of branes under consideration

Summary

Introduction

G of the corresponding (D − 2), (D − 1) and D-form potentials, resprectively. This can be understood from a group-theoretic viewpoint by observing that the components of the potentials that couple to branes correspond to the long weights of the representation [19], and in the maximal theory only the (D − 2), (D − 1) and D-form potentials belong to representations whose weights have different lengths. We show that from the same T-duality rules, when applied to all the other potentials of IIA and IIB that correspond to branes in lower dimensions without a ten-dimensional brane origin, one derives a set of generalised wrapping rules that allow to determine the number of all the branes in any dimension.

Results

Conclusion