Off- and on-shell harmonic superspaces for 6D SYM theories

TL;DR

This paper discusses harmonic superspace formulations for 6D supersymmetric Yang-Mills theories, highlighting their utility in constructing invariants and understanding divergence structures in these theories.

Contribution

It introduces an on-shell harmonic superspace approach for 6D { m N}=(1,1) SYM, aiding in the analysis of counterterms and invariants.

Findings

On-shell { m N}=(1,1) harmonic superspace helps identify differences between invariants.

The approach explains the absence of certain non-planar counterterms.

Superspace constraints are solved in terms of { m N}=(1,0) superfields.

Abstract

It is a brief account of the harmonic superspace formulations of {\cal N}=(1,0) and {\cal N}=(1,1) SYM theories in six dimensions. The on-shell {\cal N}=(1,1) harmonic superspace is argued to provide an efficient tool of constructing candidate counterterms and other invariants of {\cal N}=(1,1) SYM. It allows one, e.g., to find out an essential difference between the single- and double-trace dimension d=10 invariants, which could be capable to explain the absence of the three-loop double-trace (non-planar) counterterms in this theory. The defining superspace constraints of {\cal N}=(1,1) SYM are solved in terms of {\cal N}=(1,0) harmonic superfields.