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Physics Letters B 802 (2020) 135218
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Quantum calculation of the low-energy effective action in 5D, N =2
SYM
theory
I.L. Buchbinder
a,b
, E.A. Ivanov
c
, B.S. Merzlikin
d,a,∗
a
Department of Theoretical Physics, Tomsk State Pedagogical University, 634061, Tomsk, Russia
b
National Research Tomsk State University, 634050, Tomsk, Russia
c
Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow region, Russia
d
Tomsk State University of Control Systems and Radioelectronics, 634050 Tomsk, Russia
a r t i c l e i n f o a b s t r a c t
Article history:
Received
19 December 2019
Accepted
13 January 2020
Available
online 15 January 2020
Editor:
N. Lambert
We consider 5D, N = 2 supersymmetric Yang-Mills (SYM) theory in 5D, N = 1 harmonic superspace
as a theory of the interacting adjoint 5D, N = 1gauge multiplet and hypermultiplet. Using the
background superfield method, we compute the leading low-energy contribution to the one-loop effective
action. The result of quantum calculations precisely matches the effective action derived earlier in
arXiv:1812.07206 on the pure symmetry grounds.
© 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
The study of maximally extended supersymmetric gauge theories in dimensions larger than four is basically motivated by the relation-
ships
of such theories to the low-energy string/brane dynamics (see e.g. [1,2]). In the present paper we consider the quantum field aspects
of N = 2SYM theory in five dimensions. This theory bears an obvious interest because of its various connections with 6D, N = (2, 0)
superconformal field theory compactified on a circle [3–5] and also as a nice example of applications of the localization technique [6–10].
Quantum effective action can be thought of as a universal tool of analyzing connections between the low-energy effects in string theory
and in quantum field theory.
The
leading term of the low-energy effective action of 5D, N = 2SYM theory depending on all fields of 5D, N = 2vector gauge
multiplet was constructed in ref. [11]. This was accomplished by the method similar to that employed in [12]for a similar calculation in
4D, N = 4SYM theory. The latter was formulated in N = 2 harmonic superspace as a theory of N = 2vector gauge multiplet coupled
to the hypermultiplet in adjoint representation. Such a theory, being manifestly N = 2 supersymmetric, possesses an additional hidden
on-shell N = 2 supersymmetry. As a result, it proves to enjoy the total N = 4 supersymmetry. It was shown that the effective action
depending on both the gauge multiplet and the hypermultiplet can be found in a closed form, starting from the known effective action
in the N =2gauge multiplet sector and invoking the invariance under the hidden N =2 supersymmetry. Such a purely symmetry-based
analysis allowed to determine the effective action up to a numerical coefficient. To specify the coefficient, one should carry out the
explicit quantum calculation. The latter was performed in [13], where the result of [12]was entirely confirmed and the unknown overall
coefficient was fixed.
In
ref. [11], 5D, N = 2SYM theory was formulated in 5D, N =1 harmonic superspace as a theory of interacting N = 1gauge multiplet
and hypermultiplet in the adjoint representation. The theory is manifestly N = 1 supersymmetric and, in addition, possesses an implicit
on-shell N =1 supersymmetry. Its effective action in the N = 1gauge multiplet sector was calculated some time ago in [14]. Like in the
4D, N =4case, the total N =2 supersymmetric effective action of this theory was restored in [11]through the completion of the N =1
gauge
multiplet action by the proper hypermultiplet-dependent terms, such that the full expression for the effective action respect the
additional implicit N = 1 supersymmetry. The resulting effective action can be written as an integral over the full 5D, N = 1superspace
[11],
*
Corresponding author.
E-mail
addresses: joseph@tspu.edu.ru (I.L. Buchbinder), eivanov@theor.jinr.ru (E.A. Ivanov), merzlikin@tspu.edu.ru (B.S. Merzlikin).
https://doi.org/10.1016/j.physletb.2020.135218
0370-2693/
© 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.