Abstract
We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special case of our theories arises in the ultra-relativistic limit of a covariant parent theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J-M. Levy-Leblond, Une nouvelle limite non-relativiste du group de Poincare, Ann. Inst. Henri Poincare 3 (1965) 1.
N. D. Sen Gupta, On an analogue of the Galilei group, Nuovo Cim. 44 (1966) 512.
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. Duval, G. W. Gibbons and P. A. Horvathy, Conformal Carroll groups, J. Phys. A 47 (2014) 335204 [arXiv:1403.4213] [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].
M. Henneaux, Geometry of Zero Signature Space-times, Bull. Soc. Math. Belg. 31 (1979) 47.
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.
R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128 (1962) 2851 [INSPIRE].
G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].
G. Barnich and C. Troessaert, Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited, Phys. Rev. Lett. 105 (2010) 111103 [arXiv:0909.2617] [INSPIRE].
L. Ciambelli, R. G. Leigh, C. Marteau and P. M. Petropoulos, Carroll Structures, Null Geometry and Conformal Isometries, Phys. Rev. D 100 (2019) 046010 [arXiv:1905.02221] [INSPIRE].
L. Ciambelli, C. Marteau, A. C. Petkou, P. M. Petropoulos and K. Siampos, Flat holography and Carrollian fluids, JHEP 07 (2018) 165 [arXiv:1802.06809] [INSPIRE].
L. Ciambelli, C. Marteau, A. C. Petkou, P. M. Petropoulos and K. Siampos, Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids, Class. Quant. Grav. 35 (2018) 165001 [arXiv:1802.05286] [INSPIRE].
A. Bagchi, R. Basu, A. Mehra and P. Nandi, Field Theories on Null Manifolds, JHEP 02 (2020) 141 [arXiv:1912.09388] [INSPIRE].
A. Bagchi, A. Mehra and P. Nandi, Field Theories with Conformal Carrollian Symmetry, JHEP 05 (2019) 108 [arXiv:1901.10147] [INSPIRE].
A. Bagchi, R. Basu, A. Kakkar and A. Mehra, Flat Holography: Aspects of the dual field theory, JHEP 12 (2016) 147 [arXiv:1609.06203] [INSPIRE].
L. Ciambelli and C. Marteau, Carrollian conservation laws and Ricci-flat gravity, Class. Quant. Grav. 36 (2019) 085004 [arXiv:1810.11037] [INSPIRE].
R. M. Wald, General Relativity, University of Chicago Press, (1984) [DOI].
G. Compère, A. Fiorucci and R. Ruzziconi, The Λ-BMS4 group of dS4 and new boundary conditions for AdS4, Class. Quant. Grav. 36 (2019) 195017 [arXiv:1905.00971] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D 90 (2014) 124028 [arXiv:1408.2228] [INSPIRE].
N. Gupta and N. V. Suryanarayana, work in progress.
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [INSPIRE].
S. Banerjee, P. Pandey and P. Paul, Conformal properties of soft operators: Use of null states, Phys. Rev. D 101 (2020) 106014 [arXiv:1902.02309] [INSPIRE].
S. Banerjee and P. Pandey, Conformal properties of soft-operators. Part II. Use of null-states, JHEP 02 (2020) 067 [arXiv:1906.01650] [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: 2001.03056
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
Gupta, N., Suryanarayana, N.V. Constructing Carrollian CFTs. J. High Energ. Phys. 2021, 194 (2021). https://doi.org/10.1007/JHEP03(2021)194
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2021)194