On two-loop divergences of effective action in $6D$, $\mathcal{N}=(1,1)$ SYM theory

Abstract

We study the off-shell structure of the two-loop effective action in $6D,\mathcal{N}=(1,1)$ supersymmetric gauge theories formulated in $\mathcal{N}=(1,0)$ harmonic superspace. The off-shell effective action involving all fields of $6D,\mathcal{N}=(1,1)$ supermultiplet is constructed by the harmonic superfield background field method, which ensures both manifest gauge covariance and manifest $\mathcal{N}=(1,0)$ supersymmetry. We analyze the off-shell divergences dependent on both gauge and hypermultiplet superfields and argue that the gauge invariance of the divergences is consistent with the non-locality in harmonics. The two-loop contributions to the effective action are given by harmonic supergraphs with the background gauge and hypermultiplet superfields. The procedure is developed to operate with the harmonic-dependent superpropagators in the two-loop supergraphs within the superfield dimensional regularization. We explicitly calculate the gauge and the hypermultiplet-mixed divergences as the coefficients of $\frac{1}{{\epsilon }^2}$ and demonstrate that the corresponding expressions are non-local in harmonics.

1+25 pages, appendices added

References in corpus (10)

• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• The ultra-violet question in maximally supersymmetric field theories
• One-loop divergences in 6D, N=(1,0) SYM theory
• Chiral anomalies in higher-derivative supersymmetric 6D gauge theories
• One-loop divergences in the 6D, N=(1,0) abelian gauge theory
• The Ultraviolet Finiteness of N=8 Supergravity
• On the two-loop divergences of the 2-point hypermultiplet supergraphs for $6D$, $\mathcal{N}=(1,1)$ SYM theory
• Chiral anomalies in six dimensions from harmonic superspace
• On the two-loop divergences in 6D, $\mathcal{N}=(1,1)$ SYM theory
• Higher-dimensional invariants in $6D$ super Yang-Mills theory

Cited by in corpus (1)

• Supersymmetry at BLTP: Recent Progress in Two Directions