Higher dimensional supersymmetry in 4D superspace

TL;DR

This work develops a systematic framework to formulate higher-dimensional supersymmetric Yang–Mills theories (D=5–10) within 4D $ ext{N}=1$ superspace, enabling explicit, SUSY-preserving bulk–brane couplings and brane localized matter. By decomposing higher-D multiplets into 4D superfields (e.g., a D=5 vector into $V$ and $rac{1}{ oot 2 ext{}}$φ, D=10 into three φ_i), the authors construct explicit actions for Abelian and non-Abelian theories across D=5–10, including the necessary superpotential, Kähler-like terms, and WZW-like pieces to maintain gauge invariance. They demonstrate applications such as SUSY shining, chiral fermion localization, orbifold compactifications yielding $ ext{N}=1$ in 4D, anomaly inflow, and 5D super-Chern–Simons theory, illustrating the versatility of the formalism for beyond-the-Standard-Model model building. The work opens pathways to analyze brane fluctuations, BPS solitons, and potential extensions to supergravity, with connections to earlier off-shell formalisms and anomaly-cancellation mechanisms.

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.