On the component structure of one-loop effective actions in $6D$, ${\cal N}=(1,0)$ and ${\cal N}=(1,1)$ supersymmetric gauge theories

TL;DR

This paper investigates the one-loop effective actions in six-dimensional ${ m N}=(1,0)$ and ${ m N}=(1,1)$ supersymmetric gauge theories, focusing on divergences and low-energy contributions in component formulation.

Contribution

It provides explicit calculations of one-loop divergences and low-energy effective actions, highlighting the absence of effective potential contributions in ${ m N}=(1,1)$ SYM.

Findings

Calculated one-loop divergences in 6D supersymmetric gauge theories.

Identified low-energy contributions to the bosonic sector.

Showed no effective potential for constant scalar backgrounds in ${ m N}=(1,1)$ SYM.

Abstract

We study the six-dimensional ${\cal N}=(1,0)$ and ${\cal N}=(1,1)$ supersymmetric Yang-Mills (SYM) theories in the component formulation. The one-loop divergencies of effective action are calculated. The leading one-loop low-energy contributions to bosonic sector of effective action are found. It is explicitly demonstrated that the contribution to effective potential for the constant background scalar fields are absent in the ${\cal N}=(1,1)$ SYM theory.