Higher dimensional supersymmetry in 4D superspace

TL;DR

This paper develops a formalism to describe higher-dimensional supersymmetric Yang-Mills theories within 4D superspace, enabling easier model building with extra dimensions and brane-localized fields, with applications to various supersymmetric phenomena.

Contribution

It provides an explicit formulation of supersymmetric theories from 5 to 10 dimensions in 4D superspace, facilitating model building and analysis of brane-bulk interactions.

Findings

Formalism for supersymmetric bulk-brane interactions

Applications to orbifolds and fermion localization

Insights into anomaly inflow and super-Chern-Simons theories

Abstract

We present an explicit formulation of supersymmetric Yang-Mills theories from $\D=$ 5 to 10 dimensions in the familiar $\N=1,\D=4$ superspace. This provides the rules for globally supersymmetric model building with extra dimensions and in particular allows us to simply write down $\N=1$ SUSY preserving interactions between bulk fields and fields localized on branes. We present a few applications of the formalism by way of illustration, including supersymmetric ``shining'' of bulk fields, orbifolds and localization of chiral fermions, anomaly inflow and super-Chern-Simons theories.