Leading low-energy effective action in 6D, $$ \mathcal{N}=\left(1,1\right) $$ SYM theory

Abstract

Abstract We elaborate on the low-energy effective action of 6D, $$ \mathcal{N}=\left(1,1\right) $$ N = 1 1 supersymmetric Yang-Mills (SYM) theory in the $$ \mathcal{N}=\left(1,0\right) $$ N = 1 0 harmonic superspace formulation. The theory is described in terms of analytic $$ \mathcal{N}=\left(1,0\right) $$ N = 1 0 gauge superfield V ++ and analytic ω-hypermultiplet, both in the adjoint representation of gauge group. The effective action is defined in the framework of the background superfield method ensuring the manifest gauge invariance along with manifest $$ \mathcal{N}=\left(1,0\right) $$ N = 1 0 supersymmetry. We calculate leading contribution to the one-loop effective action using the on-shell background superfields corresponding to the option when gauge group SU(N) is broken to SU(N − 1) × ϒ(1) ⊂ SU(N). In the bosonic sector the effective action involves the structure $$ \sim \frac{F^2}{X^2} $$ ∼ F 2 X 2 , where F 4 is a monomial of the fourth degree in an abelian field strength F M N and X stands for the scalar fields from the ω-hypermultiplet. It is manifestly demonstrated that the expectation values of the hypermultiplet scalar fields play the role of a natural infrared cutoff.