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

TL;DR

This paper computes the leading one-loop low-energy effective action in 6D, ${ m N}=(1,1)$ supersymmetric Yang-Mills theory using harmonic superspace, revealing the structure involving gauge fields and hypermultiplet scalars.

Contribution

It provides the first explicit calculation of the one-loop effective action in 6D, ${ m N}=(1,1)$ SYM within the harmonic superspace framework, highlighting the role of hypermultiplet scalars as an infrared cutoff.

Findings

Effective action includes a $rac{F^4}{X^2}$ structure.

Hypermultiplet scalar expectation values act as infrared cutoff.

Calculation performed for gauge group breaking $SU(N) o SU(N-1) imes U(1)$.

Abstract

We elaborate on the low-energy effective action of $6D,\,{\cal N}=(1,1)$ supersymmetric Yang-Mills (SYM) theory in the ${\cal N}=(1,0)$ harmonic superspace formulation. The theory is described in terms of analytic ${\cal N}=(1,0)$ 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 ${\cal N}=(1,0)$ 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.