Abstract
We study the one loop renormalization group flow of the marginal deformations of \( \mathcal{N}=4 \) SYM theory using the a-function. We found that in the planar limit some non-supersymmetric deformations flow to the supersymmetric infrared fixed points described by the Leigh-Strassler theory. This means supersymmetry emerges as a result of renormalization group flow.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T. Grover, D.N. Sheng and A. Vishwanath, Emergent space-time supersymmetry at the boundary of a topological phase, Science 344 (2014) 280 [arXiv:1301.7449] [INSPIRE].
O. Antipin, M. Mojaza, C. Pica and F. Sannino, Magnetic fixed points and emergent supersymmetry, JHEP 06 (2013) 037 [arXiv:1105.1510] [INSPIRE].
L. Huijse, B. Bauer and E. Berg, Emergent supersymmetry at the Ising-Berezinskii-Kosterlitz-Thouless multicritical point, Phys. Rev. Lett. 114 (2015) 090404 [arXiv:1403.5565] [INSPIRE].
R.G. Leigh and M.J. Strassler, Exactly marginal operators and duality in four-dimensional N = 1 supersymmetric gauge theory, Nucl. Phys. B 447(1995) 95 [hep-th/9503121] [INSPIRE].
D.J. Wallace and R.K.P. Zia, Gradient flow and the renormalization group, Phys. Lett. A 48 (1974) 325 [INSPIRE].
D.Z. Freedman and H. Osborn, Constructing a c function for SUSY gauge theories, Phys. Lett. B 432 (1998) 353 [hep-th/9804101] [INSPIRE].
A.B. Zamolodchikov, Irreversibility of the flux of the renormalization group in a 2D field theory, JETP Lett. 43 (1986) 730 [Pisma Zh. Eksp. Teor. Fiz. 43 (1986) 565] [INSPIRE].
A.B. Zamolodchikov, Renormalization group and perturbation theory near fixed points in two-dimensional field theory, Sov. J. Nucl. Phys. 46 (1987) 1090 [Yad. Fiz. 46 (1987) 1819] [INSPIRE].
D. Kutasov, New results on the ‘a theorem’ in four-dimensional supersymmetric field theory, hep-th/0312098 [INSPIRE].
J. Babington and J. Erdmenger, Space-time dependent couplings in N = 1 SUSY gauge theories: anomalies and central functions, JHEP 06 (2005) 004 [hep-th/0502214] [INSPIRE].
Z. Komargodski and A. Schwimmer, On renormalization group flows in four dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987] [INSPIRE].
Z. Komargodski, The constraints of conformal symmetry on RG flows, JHEP 07 (2012) 069 [arXiv:1112.4538] [INSPIRE].
J.-F. Fortin, B. Grinstein and A. Stergiou, Limit cycles in four dimensions, JHEP 12 (2012) 112 [arXiv:1206.2921] [INSPIRE].
I. Jack and H. Osborn, Constraints on RG flow for four dimensional quantum field theories, Nucl. Phys. B 883 (2014) 425 [arXiv:1312.0428] [INSPIRE].
A. Ramos, The gradient flow running coupling with twisted boundary conditions, JHEP 11 (2014) 101 [arXiv:1409.1445] [INSPIRE].
I. Jack and C. Poole, The a-function for gauge theories, JHEP 01 (2015) 138 [arXiv:1411.1301] [INSPIRE].
M.-X. Luo, H.-W. Wang and Y. Xiao, Two loop renormalization group equations in general gauge field theories, Phys. Rev. D 67 (2003) 065019 [hep-ph/0211440] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Deformations of superconformal theories, arXiv:1602.01217 [INSPIRE].
D. Green, Z. Komargodski, N. Seiberg, Y. Tachikawa and B. Wecht, Exactly marginal deformations and global symmetries, JHEP 06 (2010) 106 [arXiv:1005.3546] [INSPIRE].
D. Anselmi, D.Z. Freedman, M.T. Grisaru and A.A. Johansen, Nonperturbative formulas for central functions of supersymmetric gauge theories, Nucl. Phys. B 526 (1998) 543 [hep-th/9708042] [INSPIRE].
D. Anselmi, J. Erlich, D.Z. Freedman and A.A. Johansen, Positivity constraints on anomalies in supersymmetric gauge theories, Phys. Rev. D 57 (1998) 7570 [hep-th/9711035] [INSPIRE].
E. Barnes, K.A. Intriligator, B. Wecht and J. Wright, Evidence for the strongest version of the 4d a-theorem, via a-maximization along RG flows, Nucl. Phys. B 702 (2004) 131 [hep-th/0408156] [INSPIRE].
L.V. Bork, D.I. Kazakov, G.S. Vartanov and A.V. Zhiboedov, Conformal invariance in the Leigh-Strassler deformed N = 4 SYM theory, JHEP 04 (2008) 003 [arXiv:0712.4132] [INSPIRE].
S.A. Frolov, R. Roiban and A.A. Tseytlin, Gauge-string duality for (non)supersymmetric deformations of N = 4 super Yang-Mills theory, Nucl. Phys. B 731 (2005) 1 [hep-th/0507021] [INSPIRE].
S. Frolov, Lax pair for strings in Lunin-Maldacena background, JHEP 05 (2005) 069 [hep-th/0503201] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1601.01943
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Jin, Q. Emergent supersymmetry in the marginal deformations of \( \mathcal{N}=4 \) SYM. J. High Energ. Phys. 2016, 131 (2016). https://doi.org/10.1007/JHEP10(2016)131
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2016)131