Leading low-energy effective action in 6D, N=11 $$ \mathcal{N}=\left(1,1\right) $$ SYM theory

Abstract

Abstract We elaborate on the low-energy effective action of 6D, N=11 $$ \mathcal{N}=\left(1,1\right) $$ supersymmetric Yang-Mills (SYM) theory in the N=10 $$ \mathcal{N}=\left(1,0\right) $$ harmonic superspace formulation. The theory is described in terms of analytic N=10 $$ \mathcal{N}=\left(1,0\right) $$ 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 N=10 $$ \mathcal{N}=\left(1,0\right) $$ 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 ∼F2X2 $$ \sim \frac{F^2}{X^2} $$ , 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.

Keywords

• Extended Supersymmetry
• Superspaces
• Supersymmetric Gauge Theory