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

Abstract

We elaborate on the low-energy effective action of $6D,\mathcal{N}=(1,1)$ supersymmetric Yang-Mills (SYM) theory in the $\mathcal{N}=(1,0)$ harmonic superspace formulation. The theory is described in terms of analytic $\mathcal{N}=(1,0)$ gauge superfield $V^{++}$ and analytic $\omega$-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 $\mathcal{N}=(1,0)$ 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 $SU(N-1)\times U(1)\subset SU(N)$. In the bosonic sector the effective action involves the structure $\sim \frac{F^4}{X^2}$, where $F^4$ is a monomial of the fourth degree in an abelian field strength $F_{MN}$ and $X$ stands for the scalar fields from the $\omega$-hypermultiplet. It is manifestly demonstrated that the expectation values of the hypermultiplet scalar fields play the role of a natural infrared cutoff.

1+14 pages, text essentially remade, some references added, title is slightly corrected

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Cited by in corpus (5)

• On the component structure of one-loop effective actions in $6D$, $\mathcal{N}=(1,0)$ and $\mathcal{N}=(1,1)$ supersymmetric gauge theories
• On two-loop divergences of effective action in $6D$, $\mathcal{N}=(1,1)$ SYM theory
• Superfield realization of hidden $R$-symmetry in extended supersymmetric gauge theories and its applications
• Dual Conformal Symmetry and Iterative Integrals in Six Dimensions
• Supersymmetry at BLTP: Recent Progress in Two Directions