Low-energy $6D$, ${\cal N}=(1,1)$ SYM effective action beyond the leading approximation

Abstract: For $6D$, ${\cal N}=(1,1)$ SYM theory formulated in ${\cal N}=(1,0)$ harmonic superspace as a theory of interacting gauge multiplet and hypermultiplet we construct the ${\cal N}=(1,1)$ supersymmetric Heisenberg-Euler-type superfield effective action. The effective action is computed for the slowly varying on-shell background fields and involves, in the bosonic sector, all powers of a constant abelian strength.