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SUMMARY:Superfield realization of hidden R-symmetry in extended supersymme
tric gauge theories and its applications
DTSTART;VALUE=DATE-TIME:20200305T183600Z
DTEND;VALUE=DATE-TIME:20200305T184800Z
DTSTAMP;VALUE=DATE-TIME:20210624T150832Z
UID:indico-contribution-270@rich2018.org
DESCRIPTION:Speakers: Viacheslav Ivanovskiy (MIPT)\nAn object of the cruci
al importance in quantum field theory is the effective action. By definiti
on\, it is a generating functional for one-particle irreducible Green's fu
nctions\, which contains complete information about the quantum properties
of this model. To find an effective action\, it is convenient to use the
technique of harmonic superspace.\n\nSuperspace[1] is a generalization of
Minkowski space and allows explicitly and in a simple form to implement su
persymmetry transformations. In theories with extended supersymmetry\, the
concept of harmonic superspace[2] plays an important role\, which allows
one to realize the symmetries of the theory off shell. Its important prope
rty is the presence of an analytic subspace invariant with respect to supe
rsymmetry.\n\nWhen studying $4D\, \\mathcal N = 4$\, and $5D\, \\mathcal N
= 2$ of supersymmetric Yang-Mills theories in harmonic superspace\, some
of the transformations of supersymmetry and\, accordingly\, $R$-symmetry a
re realized hiddenly[3\,4]. The standard approach for obtaining low-energy
effective action is as follows[4\,5]. First\, the leading one-loop quantu
m corrections for to the effective actions of $4D\, \\mathcal N = 2$ and
$5D\, \\mathcal N = 1$ SYM theories are calculated. Then\, by calculating
the expansion of this contribution with respect to hidden supersymmetry\,
expression is obtained for the effective action for $ 4D\, \\mathcal N = 4
$\, and $5D\, \\mathcal N = 2$ theories\, respectively.\n\nIn this paper\,
a different approach is used. The hidden $R$-symmetry transformations was
found. Then\, by calculating the expansion of the leading term with respe
ct to $R$-symmetry\, the expression for the effective action was obtained
. This procedure was applied for $4D\, \\mathcal N = 4$ and $5D\, \\mathc
al N = 2$ SYM theories. The nontrivial result is that the effective action
is not only $R$-symmetric invariant\, but can also be obtained from the r
equirement of the presence of $R$-symmetry.\n\nIt is expected that this ap
proach may be useful in the study of other supersymmetric theories\, for e
xample\, $6D\, \\mathcal N=(2\,0)$ SYM theory.\n\nThis reseerch based on t
he parer[6].\n\nReferences\n1. I. L. Buchbinder\, S. M. Kuzenko. Ideas and
Methods of Supersymmetry and Supergravity or a Walk\nthrough Superspace//
(IOP\, Bristol\, UK\, 1995).\n2. A.S. Galperin\, E.A. Ivanov\, V.I. Ogiev
etsky\, E.S. Sokatchev. Harmonic superspace//Cambridge\, UK: Univ. Pr. (20
01)\n3. I.L. Buchbinder\, E.A. Ivanov \, I.B. Samsonov. Low-energy effecti
ve action in 5D\, N=2\nsupersymmetric gauge theory//Nucl. Phys. B 940 (201
9) 54–62\n4. I. L. Buchbinder\, E. A. Ivanov\, I. B. Samsonov. The Low-E
nergy N=4 SYM Effective Action in Diverse Harmonic Superspaces// Phys. Par
t. Nucl. 48 (3) (2017) 333\n5. I. L. Buchbinder and E. A. Ivanov. Complete
N = 4 structure of low-energy effective action in N = 4 super Yang-Mills
theories// Phys. Lett. B 524\, 208 (2002) \n6. I.L. Buchbinder\, E.A.
Ivanov\, V.A. Ivanovskiy. Superfield realization of hidden R-symmetry in
extended supersymmetric gauge theories and its applications. arXiv:2001.0
1649 [hep-th]\n\nhttps://mosphys.ru/indico/event/5/contributions/270/
LOCATION:HSE Study Center “Voronovo”
URL:https://mosphys.ru/indico/event/5/contributions/270/
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