Higher-dimensional invariants in 6D super Yang-Mills theory

Abstract

Abstract We exploit the 6D,$$ \mathcal{N} $$ N = (1, 0) and $$ \mathcal{N} $$ N = (1, 1) harmonic superspace approaches to construct the full set of the maximally supersymmetric on-shell invariants of the canonical dimension d = 12 in 6D,$$ \mathcal{N} $$ N = (1, 1) supersymmetric Yang-Mills (SYM) theory. Both single- and double-trace invariants are derived. Only four single-trace and two double-trace invariants prove to be independent. The invariants constructed can provide the possible counterterms of $$ \mathcal{N} $$ N = (1, 1) SYM theory at four-loop order, where the first double-trace divergences are expected to appear. We explicitly exhibit the gauge sector of all invariants in terms of $$ \mathcal{N} $$ N = (1, 0) gauge superfields and find the absence of $$ \mathcal{N} $$ N = (1, 1) supercompletion of the F6 term in the abelian limit.