Weyl versus conformal invariance in quantum field theory

Farnsworth, Kara; Luty, Markus A.; Prilepina, Valentina

doi:10.1007/jhep10(2017)170

Weyl versus conformal invariance in quantum field theory

Journal Article · Tue Oct 24 00:00:00 EDT 2017 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep10(2017)170· OSTI ID:1505198

Farnsworth, Kara ^[1]; Luty, Markus A. ^[2]; Prilepina, Valentina ^[2]

Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP), Dept. of Physics; University of California, Davis
Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP), Dept. of Physics

We argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions d ≤ 10. We also study possible curvature corrections to the Weyl transformations of operators, and show that these are absent for operators of sufficiently low dimensionality and spin. We find possible ‘anomalous’ Weyl transformations proportional to the Weyl (Cotton) tensor for d > 3 (d = 3). The arguments are based on algebraic consistency conditions similar to the Wess-Zumino consistency conditions that classify possible local anomalies. The arguments can be straightforwardly extended to larger operator dimensions and higher d with additional algebraic complexity.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of California, Davis, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-91ER40674

OSTI ID:: 1505198

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 10 Vol. 2017; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

References (52)

The conformal invariance in quantum field theory Wess, J. Il Nuovo Cimento, Vol. 18, Issue 6 https://doi.org/10.1007/bf02733168	journal	December 1960
The a-theorem and the asymptotics of 4D quantum field theory Luty, Markus A.; Polchinski, Joseph; Rattazzi, Riccardo Journal of High Energy Physics, Vol. 2013, Issue 1 https://doi.org/10.1007/jhep01(2013)152	journal	January 2013
Weyl symmetry and the Liouville theory Jackiw, R. Theoretical and Mathematical Physics, Vol. 148, Issue 1 https://doi.org/10.1007/s11232-006-0090-9	journal	July 2006
Consequences of anomalous ward identities Wess, J.; Zumino, B. Physics Letters B, Vol. 37, Issue 1 https://doi.org/10.1016/0370-2693(71)90582-x	journal	November 1971
Scale and conformal invariance in quantum field theory Polchinski, Joseph Nuclear Physics B, Vol. 303, Issue 2 https://doi.org/10.1016/0550-3213(88)90179-4	journal	June 1988
Scale Invariance, Conformal Invariance, and the High-Energy Behavior of Scattering Amplitudes Gross, David J.; Wess, J. Physical Review D, Vol. 2, Issue 4 https://doi.org/10.1103/physrevd.2.753	journal	August 1970
Restricted Weyl invariance in four-dimensional curved spacetime Edery, Ariel; Nakayama, Yu Physical Review D, Vol. 90, Issue 4 https://doi.org/10.1103/physrevd.90.043007	journal	August 2014
Weyl and Ricci gauging from the coset construction Karananas, Georgios K.; Monin, Alexander arXiv https://doi.org/10.48550/arxiv.1510.07589	text	January 2015
Weyl vs. Conformal Karananas, Georgios K.; Monin, Alexander arXiv https://doi.org/10.48550/arxiv.1510.08042	text	January 2015
All unitary ray representations of the conformal group SU(2,2) with positive energy Mack, G. Communications in Mathematical Physics, Vol. 55, Issue 1 https://doi.org/10.1007/BF01613145	journal	February 1977
The conformal invariance in quantum field theory Wess, J. Il Nuovo Cimento, Vol. 18, Issue 6 https://doi.org/10.1007/BF02733168	journal	December 1960
Trace anomalies in dimensional regularization Capper, D. M.; Duff, M. J. Il Nuovo Cimento A, Vol. 23, Issue 1 https://doi.org/10.1007/BF02748300	journal	September 1974
The a-theorem and the asymptotics of 4D quantum field theory Luty, Markus A.; Polchinski, Joseph; Rattazzi, Riccardo Journal of High Energy Physics, Vol. 2013, Issue 1 https://doi.org/10.1007/JHEP01(2013)152	journal	January 2013
Limit cycles and conformal invariance Fortin, Jean-François; Grinstein, Benjamín; Stergiou, Andreas Journal of High Energy Physics, Vol. 2013, Issue 1 https://doi.org/10.1007/JHEP01(2013)184	journal	January 2013
Scale invariance, conformality, and generalized free fields Dymarsky, Anatoly; Farnsworth, Kara; Komargodski, Zohar Journal of High Energy Physics, Vol. 2016, Issue 2 https://doi.org/10.1007/JHEP02(2016)099	journal	February 2016
Free □ k scalar conformal field theory Brust, Christopher; Hinterbichler, Kurt Journal of High Energy Physics, Vol. 2017, Issue 2 https://doi.org/10.1007/JHEP02(2017)066	journal	February 2017
The local Callan-Symanzik equation: structure and applications Baume, Florent; Keren-Zur, Boaz; Rattazzi, Riccardo Journal of High Energy Physics, Vol. 2014, Issue 8 https://doi.org/10.1007/JHEP08(2014)152	journal	August 2014
Conformal symmetry of the critical 3D Ising model inside a sphere Cosme, Catarina; Lopes, J. M. Viana Parente; Penedones, João Journal of High Energy Physics, Vol. 2015, Issue 8 https://doi.org/10.1007/JHEP08(2015)022	journal	August 2015
Constraints on perturbative RG flows in six dimensions Stergiou, Andreas; Stone, David; Vitale, Lorenzo G. Journal of High Energy Physics, Vol. 2016, Issue 8 https://doi.org/10.1007/JHEP08(2016)010	journal	August 2016
Precision islands in the Ising and O(N ) models Kos, Filip; Poland, David; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2016, Issue 8 https://doi.org/10.1007/JHEP08(2016)036	journal	August 2016
On renormalization group flows and the a-theorem in 6d Elvang, Henriette; Freedman, Daniel Z.; Hung, Ling-Yan Journal of High Energy Physics, Vol. 2012, Issue 10 https://doi.org/10.1007/JHEP10(2012)011	journal	October 2012
On scale and conformal invariance in four dimensions Dymarsky, Anatoly; Komargodski, Zohar; Schwimmer, Adam Journal of High Energy Physics, Vol. 2015, Issue 10 https://doi.org/10.1007/JHEP10(2015)171	journal	October 2015
Anomalies, renormalization group flows, and the a-theorem in six-dimensional (1, 0) theories Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth Journal of High Energy Physics, Vol. 2016, Issue 10 https://doi.org/10.1007/JHEP10(2016)080	journal	October 2016
Finite-component field representations of the conformal group Mack, G.; Salam, Abdus Annals of Physics, Vol. 53, Issue 1 https://doi.org/10.1016/0003-4916(69)90278-4	journal	June 1969
A new improved energy-momentum tensor Callan, Curtis G.; Coleman, Sidney; Jackiw, Roman Annals of Physics, Vol. 59, Issue 1 https://doi.org/10.1016/0003-4916(70)90394-5	journal	July 1970
Why dilatation generators do not generate dilatations Coleman, Sidney; Jackiw, Roman Annals of Physics, Vol. 67, Issue 2 https://doi.org/10.1016/0003-4916(71)90153-9	journal	October 1971
Consequences of anomalous ward identities Wess, J.; Zumino, B. Physics Letters B, Vol. 37, Issue 1 https://doi.org/10.1016/0370-2693(71)90582-X	journal	November 1971
Geometric classification of conformal anomalies in arbitrary dimensions Deser, S.; Schwimmer, A. Physics Letters B, Vol. 309, Issue 3-4 https://doi.org/10.1016/0370-2693(93)90934-A	journal	July 1993
Non-local conformal anomalies Deser, S.; Duff, M. J.; Isham, C. J. Nuclear Physics B, Vol. 111, Issue 1 https://doi.org/10.1016/0550-3213(76)90480-6	journal	August 1976
Consistent and covariant anomalies in gauge and gravitational theories Bardeen, William A.; Zumino, Bruno Nuclear Physics B, Vol. 244, Issue 2 https://doi.org/10.1016/0550-3213(84)90322-5	journal	October 1984
On the stress tensor of conformal field theories in higher dimensions Cappelli, Andrea; Coste, Antoine Nuclear Physics B, Vol. 314, Issue 3 https://doi.org/10.1016/0550-3213(89)90414-8	journal	March 1989
Analogs of the c-theorem for four-dimensional renormalisable field theories Jack, I.; Osborn, H. Nuclear Physics B, Vol. 343, Issue 3 https://doi.org/10.1016/0550-3213(90)90584-Z	journal	October 1990
Weyl consistency conditions and a local renormalisation group equation for general renormalisable field theories Osborn, H. Nuclear Physics B, Vol. 363, Issue 2-3 https://doi.org/10.1016/0550-3213(91)80030-P	journal	October 1991
Weyl gauging and conformal invariance Iorio, A.; O'Raifeartaigh, L.; Sachs, I. Nuclear Physics B, Vol. 495, Issue 1-2 https://doi.org/10.1016/S0550-3213(97)00190-9	journal	June 1997
What Maxwell theory in teaches us about scale and conformal invariance El-Showk, Sheer; Nakayama, Yu; Rychkov, Slava Nuclear Physics B, Vol. 848, Issue 3 https://doi.org/10.1016/j.nuclphysb.2011.03.008	journal	July 2011
Weyl vs. conformal Karananas, Georgios K.; Monin, Alexander Physics Letters B, Vol. 757 https://doi.org/10.1016/j.physletb.2016.04.001	journal	June 2016
Scale invariance vs conformal invariance Nakayama, Yu Physics Reports, Vol. 569 https://doi.org/10.1016/j.physrep.2014.12.003	journal	March 2015
Conformally invariant powers of the Laplacian — A complete nonexistence theorem Gover, A. Rod; Hirachi, Kengo Journal of the American Mathematical Society, Vol. 17, Issue 2, p. 389-405 https://doi.org/10.1090/S0894-0347-04-00450-3	journal	January 2004
Restricted Weyl invariance in four-dimensional curved spacetime Edery, Ariel; Nakayama, Yu Physical Review D, Vol. 90, Issue 4 https://doi.org/10.1103/PhysRevD.90.043007	journal	August 2014
Weyl and Ricci gauging from the coset construction Karananas, Georgios K.; Monin, Alexander Physical Review D, Vol. 93, Issue 6 https://doi.org/10.1103/PhysRevD.93.064013	journal	March 2016
Conformally Invariant Powers of the Laplacian, II: Nonexistence Graham, C. Robin Journal of the London Mathematical Society, Vol. s2-46, Issue 3 https://doi.org/10.1112/jlms/s2-46.3.566	journal	December 1992
All unitary ray representations of the conformal group SU(2,2) with positive energy Mack, Gerhard Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-11746	text	January 1975
Higher symmetries of the Laplacian Eastwood, Michael Annals of Mathematics, Vol. 161, Issue 3 https://doi.org/10.4007/annals.2005.161.1645	journal	January 2005
Restrictions imposed by superconformal invariance on quantum field theories Minwalla, Shiraz Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 4 https://doi.org/10.4310/ATMP.1998.v2.n4.a4	journal	January 1998
The local Callan-Symanzik equation: structure and applications Baume, Florent; Keren-Zur, Boaz; Rattazzi, Riccardo arXiv https://doi.org/10.48550/arxiv.1401.5983	text	January 2014
Scale Invariance, Conformality, and Generalized Free Fields Dymarsky, Anatoly; Farnsworth, Kara; Komargodski, Zohar arXiv https://doi.org/10.48550/arxiv.1402.6322	preprint	January 2014
Conformal symmetry of the critical 3D Ising model inside a sphere Cosme, Catarina; Lopes, J. M. Viana Parente; Penedones, Joao arXiv https://doi.org/10.48550/arxiv.1503.02011	text	January 2015
Precision Islands in the Ising and $O(N)$ Models Kos, Filip; Poland, David; Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1603.04436	text	January 2016
Higher Symmetries of the Laplacian Eastwood, Michael arXiv https://doi.org/10.48550/arxiv.hep-th/0206233	text	January 2002
Weyl Symmetry and the Liouville Theory Jackiw, R. arXiv https://doi.org/10.48550/arxiv.hep-th/0511065	text	January 2005
Geometric Classification of Conformal Anomalies in Arbitrary Dimensions Deser, S.; Schwimmer, A. arXiv https://doi.org/10.48550/arxiv.hep-th/9302047	text	January 1993
Restrictions Imposed by Superconformal Invariance on Quantum Field Theories Minwalla, Shiraz arXiv https://doi.org/10.48550/arxiv.hep-th/9712074	text	January 1997

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