Abstract
Lagrangian gauge theories with a z = 2 Lifshitz scaling provide a family of interacting, asymptotically free five-dimensional field theories. We examine a broad class of these theories, including some of their quantum properties, extending previous results to include matter. We present no-go theorems that, in the absence of constraints, the class of theories we consider cannot admit a spinorial supersymmetry or Galilean boost symmetry. However, we argue that there exist renormalization group flows whose fixed points can admit supersymmetry and boosts, i.e. super-Schrödinger symmetry. We also present examples of Lifshitz gauge theories with a scalar supersymmetry.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Horava, Quantum criticality and Yang-Mills gauge theory, Phys. Lett. B 694 (2011) 172 [arXiv:0811.2217] [INSPIRE].
R. Iengo, J.G. Russo and M. Serone, Renormalization group in Lifshitz-type theories, JHEP 11 (2009) 020 [arXiv:0906.3477] [INSPIRE].
R. Iengo and M. Serone, A simple UV-completion of QED in 5D, Phys. Rev. D 81 (2010) 125005 [arXiv:1003.4430] [INSPIRE].
T. Kanazawa and A. Yamamoto, Asymptotically free lattice gauge theory in five dimensions, Phys. Rev. D 91 (2015) 074508 [arXiv:1411.4667] [INSPIRE].
N. Lambert and M. Owen, Non-Lorentzian field theories with maximal supersymmetry and moduli space dynamics, JHEP 10 (2018) 133 [arXiv:1808.02948] [INSPIRE].
N. Lambert and T. Orchard, Non-Lorentzian avatars of (1, 0) theories, arXiv:2011.06968 [https://doi.org/10.1007/JHEP02(2021)205] [INSPIRE].
N. Lambert, A. Lipstein, R. Mouland and P. Richmond, Bosonic symmetries of (2, 0) DLCQ field theories, JHEP 01 (2020) 166 [arXiv:1912.02638] [INSPIRE].
O. Aharony et al., Matrix description of interacting theories in six-dimensions, Adv. Theor. Math. Phys. 1 (1998) 148 [hep-th/9707079] [INSPIRE].
O. Aharony, M. Berkooz and N. Seiberg, Light cone description of (2, 0) superconformal theories in six-dimensions, Adv. Theor. Math. Phys. 2 (1998) 119 [hep-th/9712117] [INSPIRE].
N. Lambert, A. Lipstein and P. Richmond, Non-Lorentzian M5-brane theories from holography, JHEP 08 (2019) 060 [arXiv:1904.07547] [INSPIRE].
N. Lambert, A. Lipstein, R. Mouland and P. Richmond, Five-dimensional non-Lorentzian conformal field theories and their relation to six-dimensions, JHEP 03 (2021) 053 [arXiv:2012.00626] [INSPIRE].
G. Parisi and N. Sourlas, Supersymmetric field theories and stochastic differential equations, Nucl. Phys. B 206 (1982) 321 [INSPIRE].
S. Chapman, Y. Oz and A. Raviv-Moshe, On supersymmetric Lifshitz field theories, JHEP 10 (2015) 162 [arXiv:1508.03338] [INSPIRE].
I. Arav, Y. Oz and A. Raviv-Moshe, Holomorphic structure and quantum critical points in supersymmetric Lifshitz field theories, JHEP 11 (2019) 064 [arXiv:1908.03220] [INSPIRE].
L.F. Abbott, Introduction to the background field method, Acta Phys. Polon. B 13 (1982) 33 [INSPIRE].
L. Casarin, On higher-derivative gauge theories, M.Sc. thesis, Padua U., Padua, Italy (2017) [arXiv:1710.08021] [INSPIRE].
M. Namiki et al., Stochastic quantization, Lect. Notes Phys. Monogr. 9 (1992) 1 [INSPIRE].
Z. Bern, M.B. Halpern and L. Sadun, Continuum regularization of quantum field theory. 3. The QCD in four-dimensions beta function, Nucl. Phys. B 284 (1987) 92 [INSPIRE].
K. Okano, Background field method in stochastic quantization, Nucl. Phys. B 289 (1987) 109 [INSPIRE].
M.L. Bellac and J.M. Lévy-Leblond, Galilean electromagnetism, Nuovo Cim. 14 (1973) 217.
E.S. Santos, M. de Montigny, F.C. Khanna and A.E. Santana, Galilean covariant Lagrangian models, J. Phys. A 37 (2004) 9771 [INSPIRE].
G. Festuccia, D. Hansen, J. Hartong and N.A. Obers, Symmetries and couplings of non-relativistic electrodynamics, JHEP 11 (2016) 037 [arXiv:1607.01753] [INSPIRE].
C.R. Hagen, Scale and conformal transformations in galilean-covariant field theory, Phys. Rev. D 5 (1972) 377 [INSPIRE].
N. Lambert and R. Mouland, Non-Lorentzian RG flows and supersymmetry, JHEP 06 (2019) 130 [arXiv:1904.05071] [INSPIRE].
J. Gomis, J. Gomis and K. Kamimura, Non-relativistic superstrings: a new soluble sector of AdS5 × S5, JHEP 12 (2005) 024 [hep-th/0507036] [INSPIRE].
B. Mcclain, A. Niemi, C. Taylor and L.C.R. Wijewardhana, Superspace, dimensional reduction, and stochastic quantization, Nucl. Phys. B 217 (1983) 430 [INSPIRE].
G. Leibbrandt and J. Williams, Split dimensional regularization for the Coulomb gauge, Nucl. Phys. B 475 (1996) 469 [hep-th/9601046] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2212.07717
Rights and permissions
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.
About this article
Cite this article
Lambert, N., Smith, J. RG flows and symmetry enhancement in five-dimensional Lifshitz gauge theories. J. High Energ. Phys. 2023, 69 (2023). https://doi.org/10.1007/JHEP03(2023)069
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2023)069