Supergraph analysis of the one-loop divergences in $6D$, $\mathcal{N}=(1,0)$ and $\mathcal{N}=(1,1)$ gauge theories

Abstract

We study the one-loop effective action for $6D,$ $\mathcal{N}=(1,0)$ supersymmetric Yang--Mills (SYM) theory with hypermultiplets and $6D,$ $\mathcal{N}=(1,1)$ SYM theory as a subclass of the former, using the off-shell formulation of these theories in $6D,$ $\mathcal{N}=(1,0)$ harmonic superspace. We develop the corresponding supergraph technique and apply it to compute the one-loop divergences in the background field method ensuring the manifest gauge invariance. We calculate the two-point Green functions of the gauge superfield and the hypermultiplet, as well as the three-point gauge-hypermultipet Green function. Using these Green functions and exploiting gauge invariance of the theory, we find the full set of the off-shell one-loop divergent contributions, including the logarithmic and power ones. Our results precisely match with those obtained earlier in [1,2] within the proper time superfield method.

32 pages, 5 figures

References in corpus (8)

• The ultra-violet question in maximally supersymmetric field theories
• Manifestly N=2 supersymmetric regularization for N=2 supersymmetric field theories
• The higher derivative regularization and quantum corrections in $\mathcal{N}=2$ supersymmetric theories
• One-loop divergences in 6D, N=(1,0) SYM theory
• Chiral anomalies in higher-derivative supersymmetric 6D gauge theories
• Construction of 6D supersymmetric field models in N=(1,0) harmonic superspace
• One-loop divergences in the 6D, N=(1,0) abelian gauge theory
• The anomalous current multiplet in 6D minimal supersymmetry

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• Chiral anomalies in six dimensions from harmonic superspace
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