Abstract
We investigate the symmetry structure of the non-relativistic limit of Yang-Mills theories. Generalising previous results in the Galilean limit of electrodynamics, we discover that for Yang-Mills theories there are a variety of limits inside the Galilean regime. We first explicitly work with the SU(2) theory and then generalise to SU(N) for all N, systematising our notation and analysis. We discover that the whole family of limits lead to different sectors of Galilean Yang-Mills theories and the equations of motion in each sector exhibit hitherto undiscovered infinite dimensional symmetries, viz. infinite Galilean Conformal symmetries in D = 4. These provide the first examples of interacting Galilean Conformal Field Theories (GCFTs) in D > 2.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. ’t Hooft, Dimensional reduction in quantum gravity, gr-qc/9310026 [INSPIRE].
L. Susskind, The world as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
A. Bagchi, R. Basu and A. Mehra, Galilean Conformal Electrodynamics, JHEP 11 (2014) 061 [arXiv:1408.0810] [INSPIRE].
M. Le Bellac and J.M. Lévy-Leblond, Galilean Electromagnetism, Nuovo Cim. B 14 (1973) 217.
A. Bagchi and R. Gopakumar, Galilean Conformal Algebras and AdS/CFT, JHEP 07 (2009) 037 [arXiv:0902.1385] [INSPIRE].
A. Bagchi, R. Gopakumar, I. Mandal and A. Miwa, GCA in 2d, JHEP 08 (2010) 004 [arXiv:0912.1090] [INSPIRE].
H. Bondi, M.G.J. van der Burg and A.W.K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. Roy. Soc. Lond. A 269 (1962) 21 [INSPIRE].
R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128 (1962) 2851 [INSPIRE].
G. Barnich and G. Compere, Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions, Class. Quant. Grav. 24 (2007) F15 [gr-qc/0610130] [INSPIRE].
A. Bagchi, The BMS/GCA correspondence, arXiv:1006.3354 [INSPIRE].
A. Bagchi, S. Detournay and D. Grumiller, Flat-Space Chiral Gravity, Phys. Rev. Lett. 109 (2012) 151301 [arXiv:1208.1658] [INSPIRE].
A. Bagchi, S. Detournay, R. Fareghbal and J. Simón, Holography of 3D Flat Cosmological Horizons, Phys. Rev. Lett. 110 (2013) 141302 [arXiv:1208.4372] [INSPIRE].
G. Barnich, Entropy of three-dimensional asymptotically flat cosmological solutions, JHEP 10 (2012) 095 [arXiv:1208.4371] [INSPIRE].
A. Bagchi, R. Basu, D. Grumiller and M. Riegler, Entanglement entropy in Galilean conformal field theories and flat holography, Phys. Rev. Lett. 114 (2015) 111602 [arXiv:1410.4089] [INSPIRE].
G. Barnich, A. Gomberoff and H.A. González, Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory, Phys. Rev. D 87 (2013) 124032 [arXiv:1210.0731] [INSPIRE].
R. Basu and M. Riegler, Wilson Lines and Holographic Entanglement Entropy in Galilean Conformal Field Theories, Phys. Rev. D 93 (2016) 045003 [arXiv:1511.08662] [INSPIRE].
A. Bagchi, Tensionless Strings and Galilean Conformal Algebra, JHEP 05 (2013) 141 [arXiv:1303.0291] [INSPIRE].
A. Bagchi, S. Chakrabortty and P. Parekh, Tensionless Strings from Worldsheet Symmetries, JHEP 01 (2016) 158 [arXiv:1507.04361] [INSPIRE].
C. Duval, G.W. Gibbons and P.A. Horvathy, Conformal Carroll groups and BMS symmetry, Class. Quant. Grav. 31 (2014) 092001 [arXiv:1402.5894] [INSPIRE].
C. Duval and P.A. Horvathy, Non-relativistic conformal symmetries and Newton-Cartan structures, J. Phys. A 42 (2009) 465206 [arXiv:0904.0531] [INSPIRE].
A. Bagchi and I. Mandal, Supersymmetric Extension of Galilean Conformal Algebras, Phys. Rev. D 80 (2009) 086011 [arXiv:0905.0580] [INSPIRE].
M. Sakaguchi, Super Galilean conformal algebra in AdS/CFT, J. Math. Phys. 51 (2010) 042301 [arXiv:0905.0188] [INSPIRE].
J.A. de Azcarraga and J. Lukierski, Galilean Superconformal Symmetries, Phys. Lett. B 678 (2009) 411 [arXiv:0905.0141] [INSPIRE].
I. Mandal, Supersymmetric Extension of GCA in 2d, JHEP 11 (2010) 018 [arXiv:1003.0209] [INSPIRE].
H.L. Verlinde and E.P. Verlinde, QCD at high-energies and two-dimensional field theory, hep-th/9302104 [INSPIRE].
K. Jensen, Anomalies for Galilean fields, arXiv:1412.7750 [INSPIRE].
A. Jain, Galilean Anomalies and Their Effect on Hydrodynamics, Phys. Rev. D 93 (2016) 065007 [arXiv:1509.05777] [INSPIRE].
A. Bagchi and R. Fareghbal, BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries, JHEP 10 (2012) 092 [arXiv:1203.5795] [INSPIRE].
A. Bagchi, R. Basu, A. De, A. Kakkar and A. Mehra, Flat Holography: Aspects of the Dual Theory, to appear.
A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory, Nucl. Phys. B 241 (1984) 333 [INSPIRE].
R. Jackiw and S.Y. Pi, Tutorial on Scale and Conformal Symmetries in Diverse Dimensions, J. Phys. A 44 (2011) 223001 [arXiv:1101.4886] [INSPIRE].
S. El-Showk, Y. Nakayama and S. Rychkov, What Maxwell Theory in d ≠ 4 teaches us about scale and conformal invariance, Nucl. Phys. B 848 (2011) 578 [arXiv:1101.5385] [INSPIRE].
A. Bagchi and I. Mandal, On Representations and Correlation Functions of Galilean Conformal Algebras, Phys. Lett. B 675 (2009) 393 [arXiv:0903.4524] [INSPIRE].
C. Duval, G.W. Gibbons, P.A. Horvathy and P.M. Zhang, Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time, Class. Quant. Grav. 31 (2014) 085016 [arXiv:1402.0657] [INSPIRE].
C. Montonen and D.I. Olive, Magnetic Monopoles as Gauge Particles?, Phys. Lett. B 72 (1977) 117 [INSPIRE].
E. Witten, Dyons of Charge eθ/2π, Phys. Lett. B 86 (1979) 283 [INSPIRE].
N. Brambilla, A. Pineda, J. Soto and A. Vairo, Effective field theories for heavy quarkonium, Rev. Mod. Phys. 77 (2005) 1423 [hep-ph/0410047] [INSPIRE].
J. Soto, Overview of Non-Relativistic QCD, Eur. Phys. J. A 31 (2007) 705 [nucl-th/0611055] [INSPIRE].
E. Bergshoeff, J. Rosseel and T. Zojer, Non-relativistic fields from arbitrary contracting backgrounds, arXiv:1512.06064 [INSPIRE].
D. Van den Bleeken and C. Yunus, Newton-Cartan, Galileo-Maxwell and Kaluza-Klein, arXiv:1512.03799 [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: 1512.08375
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
Bagchi, A., Basu, R., Kakkar, A. et al. Galilean Yang-Mills theory. J. High Energ. Phys. 2016, 51 (2016). https://doi.org/10.1007/JHEP04(2016)051
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2016)051