5D Super Yang-Mills Theory in 4D Superspace, Superfield Brane Operators, and Applications to Orbifold GUTs

TL;DR

The paper develops a manifestly gauge-invariant 4d superfield formulation of 5d SYM by introducing a gauge- and supersymmetry-covariant derivative in the x^5 direction, ∇_5 = ∂_5 + Φ, with Φ the adjoint chiral superfield. This approach yields a compact Lagrangian in 4d superspace, with the covariant piece Z = e^{-2V}∇_5 e^{2V} and the relation L ∝ tr{ (W^α W_α)|_{θ^2} + (h.c.) + Z^2|_{θ^2ar{θ}^2} }, ensuring 5d Lorentz covariance fixes normalization relative to the 4d gauge dynamics. The framework enables systematic construction of higher-derivative operators and, in orbifold compactifications, a classification of brane-localized operators that respect the reduced symmetry at fixed points; this has direct implications for orbifold GUT phenomenology, including proton-decay operators and brane-localized mass terms. Overall, the work provides a versatile tool for analyzing bulk-bounds interactions in extra-dimensional SUSY theories and paves the way for extensions to higher dimensions and varied compactifications.

Abstract

A manifestly gauge invariant formulation of 5-dimensional supersymmetric Yang-Mills theories in terms of 4d superfields is derived. It relies on a supersymmetry and gauge-covariant derivative operator in the $x^5$ direction. This formulation allows for a systematic study of higher-derivative operators by combining invariant 4d superfield expressions under the additional restriction of 5d Lorentz symmetry. In cases where the 5d theory is compactified on a gauge-symmetry-breaking orbifold, the formalism can be used for a simple discussion of possible brane operators invariant under the restricted symmetry of the fixed points. This is particularly relevant to recently constructed grand unified theories in higher dimensions (orbifold GUTs). Several applications, including proton decay operators and brane-localized mass terms, are discussed.