Conformal Carroll groups

By C. Duval, G. W. Gibbons, P. Horváthy. 2014

233 citations recorded by the source corpus.

Conformal extensions of Lévy–Leblondʼs Carroll group, based on geometric properties analogous to those of Newton–Cartan space-time are proposed. The extensions are labeled by an integer k. This framework includes and extends our recent study of the Bondi–Metzner–Sachs (BMS) and Newman–Unti (NU) groups. The relation to conformal Galilei groups is clarified. Conformal Carroll symmetry is illustrated by ‘Carrollian photons’. Motion both in the Newton–Cartan and Carroll spaces may be related to that of strings in the Bargmann space.

Subfields: Applied Mathematics, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/4eb41ef29de893b95e2ec2dc920d150bd645c993

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Eric Bergshoeff
2. G. W. Gibbons
3. J. Hartong
4. Joaquim Gomis
5. G. Longhi
6. P. Horváthy
7. C. Duval
8. L. Donnay

In Mathematical Physics

1. J. Hartong
2. Charles Marteau
3. Joaquim Gomis
4. Eric Bergshoeff
5. G. Longhi
6. L. Donnay
7. P. Petropoulos
8. Luca Ciambelli

In Nuclear and High Energy Physics

1. J. Hartong
2. Eric Bergshoeff
3. L. Donnay
4. Adrien Fiorucci
5. Arjun Bagchi
6. Joaquim Gomis
7. Charles Marteau
8. P. Horváthy

Citations in the corpus

• Notes on the BMS group in three dimensions: II. Coadjoint representation (2015, background): “Specific coadjoints orbits of related (conformal) Carroll groups have recently also been discussed in [11, 12].”
• Bridging Carrollian and celestial holography (2022, background): “This shows that the conformal Carroll algebra in 3d is isomorphic to the BMS algebra in 4d [17, 182].”
• Carroll structures, null geometry, and conformal isometries (2019, background): “[4] no Ehresmann connection was introduced.”
• Conformal Carroll groups and BMS symmetry (2014, background): “In the flat case (i) our formulae yield [14]”
• Dynamics of Carroll particles (2014, methodology): “If we put more structure in the transverse space these transformations will have restrictions and we could obtain the Carroll trasformations of [16, 6].”
• Tensionless strings from worldsheet symmetries (2015, background): “The tensionless worldsheet, which is what the worldsheet becomes near the Hagedorn temperature, is now replaced by a Carrollian manifold [47, 48].”
• Gauging the Carroll algebra and ultra-relativistic gravity (2015, background): “Recently conformal extensions of the Carroll algebra have been studied in [13, 58] and it has been shown that the BMS algebra forms a conformal extension of the Carroll algebra [13].”