# Low-energy effective action in 5D, N=2 supersymmetric gauge theory

## TL;DR

This paper constructs the low-energy effective action for 5D, N=2 supersymmetric Yang-Mills theory using harmonic superspace, revealing an SO(5)-invariant F^4/X^3 term and applicable to various gauge symmetry breakings.

## Contribution

It provides a novel explicit construction of the 5D, N=2 supersymmetric effective action as a hypermultiplet completion, extending previous N=1 results.

## Key findings

- Derived the N=2 effective action with SO(5) invariance.
- Identified the F^4/X^3 term in the component form.
- Applicable to gauge symmetry breaking to abelian subgroups.

## Abstract

We construct ${\cal N}=2$ supersymmetric low-energy effective action of $5D, {\cal N}=2$ supersymmetric Yang-Mills theory in $5D, {\cal N}=1$ harmonic superspace. It is obtained as a hypermultiplet completion of the leading $W \ln W$-term in the ${\cal N}=1$ SYM low-energy effective action by invoking the second implicit on-shell ${\cal N}=1$ supersymmetry. After passing to components, the ${\cal N}=2$ effective action constructed displays, along with other terms, the $SO(5)$-invariant $F^4/X^3$ term. Though we specialize to the case of $SU(2)$ gauge group spontaneously broken to $U(1)$, our consideration is applicable to any gauge symmetry broken to some abelian subgroup.