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Symmetry 2019, 11(1), 68; https://doi.org/10.3390/sym11010068

Harmonic Superspace Approach to the Effective Action in Six-Dimensional Supersymmetric Gauge Theories

1
Department of Theoretical Physics, Tomsk State Pedagogical University, 634061 Tomsk, Russia
2
Division of Experimental Physics, National Research Tomsk Polytechnic University, 634050 Tomsk, Russia
3
Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow region, Russia
4
Department of Theoretical Physics, Faculty of Physics, Moscow State University, 119991 Moscow, Russia
*
Author to whom correspondence should be addressed.
Received: 11 December 2018 / Revised: 31 December 2018 / Accepted: 2 January 2019 / Published: 8 January 2019
(This article belongs to the Special Issue Supersymmetric Field Theory 2018)
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Abstract

We review the recent progress in studying the quantum structure of 6 D , N = ( 1 , 0 ) , and N = ( 1 , 1 ) supersymmetric gauge theories formulated through unconstrained harmonic superfields. The harmonic superfield approach allows one to carry out the quantization and calculations of the quantum corrections in a manifestly N = ( 1 , 0 ) supersymmetric way. The quantum effective action is constructed with the help of the background field method that secures the manifest gauge invariance of the results. Although the theories under consideration are not renormalizable, the extended supersymmetry essentially improves the ultraviolet behavior of the lowest-order loops. The N = ( 1 , 1 ) supersymmetric Yang–Mills theory turns out to be finite in the one-loop approximation in the minimal gauge. Furthermore, some two-loop divergences are shown to be absent in this theory. Analysis of the divergences is performed both in terms of harmonic supergraphs and by the manifestly gauge covariant superfield proper-time method. The finite one-loop leading low-energy effective action is calculated and analyzed. Furthermore, in the Abelian case, we discuss the gauge dependence of the quantum corrections and present its precise form for the one-loop divergent part of the effective action. View Full-Text
Keywords: supersymmetry; harmonic superspace; quantum corrections; effective action supersymmetry; harmonic superspace; quantum corrections; effective action
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Buchbinder, I.; Ivanov, E.; Merzlikin, B.; Stepanyantz, K. Harmonic Superspace Approach to the Effective Action in Six-Dimensional Supersymmetric Gauge Theories. Symmetry 2019, 11, 68.

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