### Abstract

We review the recent progress in studying the quantum structure of 6D, 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.

Original language | English |
---|---|

Article number | 68 |

Journal | Symmetry |

Volume | 11 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

### Fingerprint

### Keywords

- Effective action
- Harmonic superspace
- Quantum corrections
- Supersymmetry

### ASJC Scopus subject areas

- Computer Science (miscellaneous)
- Chemistry (miscellaneous)
- Mathematics(all)
- Physics and Astronomy (miscellaneous)

### Cite this

*Symmetry*,

*11*(1), [68]. https://doi.org/10.3390/sym11010068

**Harmonic superspace approach to the effective action in six-dimensional supersymmetric gauge theories.** / Buchbinder, Ioseph; Ivanov, Evgeny; Merzlikin, Boris; Stepanyantz, Konstantin.

Research output: Contribution to journal › Article

*Symmetry*, vol. 11, no. 1, 68. https://doi.org/10.3390/sym11010068

}

TY - JOUR

T1 - Harmonic superspace approach to the effective action in six-dimensional supersymmetric gauge theories

AU - Buchbinder, Ioseph

AU - Ivanov, Evgeny

AU - Merzlikin, Boris

AU - Stepanyantz, Konstantin

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We review the recent progress in studying the quantum structure of 6D, 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.

AB - We review the recent progress in studying the quantum structure of 6D, 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.

KW - Effective action

KW - Harmonic superspace

KW - Quantum corrections

KW - Supersymmetry

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UR - http://www.scopus.com/inward/citedby.url?scp=85061125520&partnerID=8YFLogxK

U2 - 10.3390/sym11010068

DO - 10.3390/sym11010068

M3 - Article

VL - 11

JO - Symmetry

JF - Symmetry

SN - 2073-8994

IS - 1

M1 - 68

ER -