Abstract
We elaborate on the low-energy effective action of 6D, \( \mathcal{N}=\left(1,1\right) \) supersymmetric Yang-Mills (SYM) theory in the \( \mathcal{N}=\left(1,0\right) \) harmonic superspace formulation. The theory is described in terms of analytic \( \mathcal{N}=\left(1,0\right) \) 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 \( \mathcal{N}=\left(1,0\right) \) 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 \( \sim \frac{F^2}{X^2} \) , where F 4 is a monomial of the fourth degree in an abelian field strength FM 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.
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Buchbinder, I.L., Ivanov, E.A. & Merzlikin, B.S. Leading low-energy effective action in 6D, \( \mathcal{N}=\left(1,1\right) \) SYM theory. J. High Energ. Phys. 2018, 39 (2018). https://doi.org/10.1007/JHEP09(2018)039
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DOI: https://doi.org/10.1007/JHEP09(2018)039