Ultraviolet behavior of 6D supersymmetric Yang-Mills theories and harmonic superspace

TL;DR

This paper investigates the ultraviolet properties of 6D N=(1,1) supersymmetric Yang-Mills theories using harmonic superspace, providing new methods to analyze counterterms and potential non-renormalization theorems.

Contribution

It develops a comprehensive harmonic superspace approach to solve N=(1,1) SYM constraints in terms of N=(1,0) superfields, enabling explicit construction of counterterms.

Findings

Developed a general harmonic superspace method for N=(1,1) SYM

Explicit expressions for counterterms and invariants obtained

Potential insights into non-renormalization theorems and divergence cancellations

Abstract

We revisit the issue of higher-dimensional counterterms for the N=(1,1) supersymmetric Yang-Mills (SYM) theory in six dimensions using the off-shell N=(1,0) and on-shell N=(1,1) harmonic superspace approaches. The second approach is developed in full generality and used to solve, for the first time, the N=(1,1) SYM constraints in terms of N=(1,0) superfields. This provides a convenient tool to write explicit expressions for the candidate counterterms and other N=(1,1) invariants and may be conducive to proving non-renormalization theorems needed to explain the absence of certain logarithmic divergences in higher-loop contributions to scattering amplitudes in N=(1,1) SYM.