Five-dimensional supersymmetric Chern-Simons action as a hypermultiplet quantum correction

TL;DR

This paper develops a 5D N=1 supersymmetric formalism to compute the one-loop effective action of a hypermultiplet, demonstrating the quantum generation of a supersymmetric Chern-Simons term consistent with previous component results.

Contribution

It introduces a covariant supergraph approach in 5D N=1 harmonic superspace to derive quantum corrections, including the supersymmetric Chern-Simons action.

Findings

Quantum 5D N=1 supersymmetric Chern-Simons action generated at one-loop

Formalism compatible with previous component analyses

Potential for further formulations in hybrid or projective superspace approaches

Abstract

Building on the covariant supergraph techniques in 4D N = 2 harmonic superspace, we develop a manifestly 5D N = 1 supersymmetric and gauge covariant formalism to compute the one-loop effective action for a hypermultiplet coupled to a background vector multiplet. As a simple application, we demonstrate the generation of a supersymmetric Chern-Simons action at the quantum level, both in the Coulomb and the non-Abelian phases. These superfield results are in agreement with the earlier component considerations of Seiberg et al. Our analysis suggests that similar calculations in terms of hybrid 4D superfields or within the 5D projective superspace approach may allow one to extract suitable formulations for the non-Abelian 5D supersymmetric Chern-Simons theory.