Leading low-energy effective action in 6D, \( \mathcal{N}=\left(1,1\right) \) SYM theory

Journal of High Energy Physics, Sep 2018

Abstract We elaborate on the low-energy effective action of 6D, \( \mathcal{N}=\left(1,1\right) \) supersymmetric Yang-Mills (SYM) theory in the \( \mathcal{N}=\left(1,0\right) \) harmonic superspace formulation. The theory is described in terms of analytic \( \mathcal{N}=\left(1,0\right) \) gauge superfield V ++ and analytic ω-hypermultiplet, both in the adjoint representation of gauge group. The effective action is defined in the framework of the background superfield method ensuring the manifest gauge invariance along with manifest \( \mathcal{N}=\left(1,0\right) \) supersymmetry. We calculate leading contribution to the one-loop effective action using the on-shell background superfields corresponding to the option when gauge group SU(N) is broken to SU(N − 1) × ϒ(1) ⊂ SU(N). In the bosonic sector the effective action involves the structure \( \sim \frac{F^2}{X^2} \) , where F 4 is a monomial of the fourth degree in an abelian field strength FM N and X stands for the scalar fields from the ω-hypermultiplet. It is manifestly demonstrated that the expectation values of the hypermultiplet scalar fields play the role of a natural infrared cutoff.

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Leading low-energy effective action in 6D, \( \mathcal{N}=\left(1,1\right) \) SYM theory

Journal of High Energy Physics September 2018, 2018:39 | Cite as Leading low-energy effective action in 6D, \( \mathcal{N}=\left(1,1\right) \) SYM theory AuthorsAuthors and affiliations I. L. BuchbinderE. A. IvanovB. S. Merzlikin Open Access Regular Article - Theoretical Physics First Online: 07 September 2018 Received: 14 June 2018 Revised: 16 August 2018 Accepted: 03 September 2018 14 Downloads Abstract We elaborate on the low-energy effective action of 6D, \( \mathcal{N}=\left(1,1\right) \) supersymmetric Yang-Mills (SYM) theory in the \( \mathcal{N}=\left(1,0\right) \) harmonic superspace formulation. The theory is described in terms of analytic \( \mathcal{N}=\left(1,0\right) \) gauge superfield V ++ and analytic ω-hypermultiplet, both in the adjoint representation of gauge group. The effective action is defined in the framework of the background superfield method ensuring the manifest gauge invariance along with manifest \( \mathcal{N}=\left(1,0\right) \) supersymmetry. We calculate leading contribution to the one-loop effective action using the on-shell background superfields corresponding to the option when gauge group SU(N) is broken to SU(N − 1) × ϒ(1) ⊂ SU(N). In the bosonic sector the effective action involves the structure \( \sim \frac{F^2}{X^2} \) , where F 4 is a monomial of the fourth degree in an abelian field strength FM N and X stands for the scalar fields from the ω-hypermultiplet. It is manifestly demonstrated that the expectation values of the hypermultiplet scalar fields play the role of a natural infrared cutoff. Keywords Extended Supersymmetry Superspaces Supersymmetric Gauge Theory  ArXiv ePrint: 1711.03302 Download to read the full article text Notes Open Access This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. References [1] E.I. Buchbinder, B.A. Ovrut, I.L. Buchbinder, E.A. Ivanov and S.M. Kuzenko, Low-energy effective action in N = 2 supersymmetric field theories, Phys. Part. Nucl. 32 (2001) 641 [INSPIRE]. [2] I.L. Buchbinder, E.A. Ivanov and N.G. Pletnev, Superfield approach to the construction of effective action in quantum field theory with extended supersymmetry, Phys. Part. Nucl. 47 (2016) 291 [INSPIRE].CrossRefGoogle Scholar [3] I.L. Buchbinder, E.A. Ivanov and I.B. Samsonov, The low-energy N = 4 SYM effective action in diverse harmonic superspaces, Phys. Part. Nucl. 48 (2017) 333 [arXiv:1603.02768] [INSPIRE]. [4] A. Giveon and D. Kutasov, Brane dynamics and gauge theory, Rev. Mod. Phys. 71 (1999) 983 [hep-th/9802067] [INSPIRE]. [5] R. Blumenhagen, B. Körs, D. Lüst and S. Stieberger, Four-dimensional String Compactifications with D-branes, Orientifolds and Fluxes, Phys. Rept. 445 (2007) 1 [hep-th/0610327] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [6] F. Gonzalez-Rey, B. Kulik, I.Y. Park and M. Roček, Selfdual effective action of \( \mathcal{N}=4 \) superYang-Mills, Nucl. Phys. B 544 (1999) 218 [hep-th/9810152] [INSPIRE]. [7] V. Periwal and R. von Unge, Accelerating D-branes, Phys. Lett. B 430 (1998) 71 [hep-th/9801121] [INSPIRE]. [8] F. Gonzalez-Rey and M. Roček, Nonholomorphic \( \mathcal{N}=2 \) terms in \( \mathcal{N}=4 \) SYM: One loop calculation in \( \mathcal{N}=2 \) superspace, Phys. Lett. B 434 (1998) 303 [hep-th/9804010] [INSPIRE]. [9] I.L. Buchbinder, E.I. Buchbinder, S.M. Kuzenko and B.A. Ovrut, The Background field method for N = 2 superYang-Mills theories in harmonic superspace, Phys. Lett. B 417 (1998) 61 [hep-th/9704214] [INSPIRE]. [10] I.L. Buchbinder and S.M. Kuzenko, Comments on the background field method in harmonic superspace: Nonholomorphic corrections in \( \mathcal{N}=4 \) SYM, Mod. Phys. Lett. A 13 (1998) 1623 [hep-th/9804168] [INSPIRE]. [11] E.I. Buchbinder, I.L. Buchbinder and S.M. Kuzenko, Nonholomorphic effective potential in \( \mathcal{N}=4 \) SU(N) SYM, Phys. Lett. B 446(1999) 216 [hep-th/9810239] [INSPIRE]. [12] D.A. Lowe and R. von Unge, Constraints on higher derivative operators in maximally supersymmetric gauge theory, JHEP 11 (1998) 014 [hep-th/9811017] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [13] I.L. Buchbinder, S.M. Kuzenko and A.A. Tseytlin, On low-energy effective actions in \( \mathcal{N}=2 \) , \( \mathcal{N}=4 \) superconformal theories in four-dimensions, Phys. Rev. D 62(2000) 045001 [hep-th/9911221] [INSPIRE]. [14] S.M. Kuzenko and I.N. McArthur, Effective action of N = 4 superYang-Mills: N = 2 superspace approach, Phys. Lett. B 506 (2001) 140 [hep-th/0101127] [INSPIRE]. [15] S.M. Kuzenko and I.N. McArthur, Hypermultiplet effective action: \( \mathcal{N}=2 \) superspace approach, Phys. Lett. B 513 (2001) 213 [hep-th/0105121] [INSPIRE]. [16] I.L. Buchbinder and E.A. Ivanov, Complete \( \mathcal{N}=4 \) structure of low-energy effective action in \( \mathcal{N} (...truncated)


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I. L. Buchbinder, E. A. Ivanov, B. S. Merzlikin. Leading low-energy effective action in 6D, \( \mathcal{N}=\left(1,1\right) \) SYM theory, Journal of High Energy Physics, 2018, pp. 39, Volume 2018, Issue 9, DOI: 10.1007/JHEP09(2018)039