Carroll fermions

[en] Using carefully chosen projections, we consider different Carroll limits of relativistic Dirac fermions in any spacetime dimensions. These limits define Carroll fermions of two types: electric and magnetic. The latter type transforms as a reducible but indecomposable representation of the Carroll group. We also build action principles for all Carroll fermions we introduce; in particular, in even dimensions we provide an action principle for a minimal magnetic Carroll fermion, having the same number of components as a Dirac spinor. We then explore the coupling of these fermions to magnetic Carroll gravity in both its first-order and second-order formulations.

Research center :

AGIF - Algèbre, Géométrie et Interactions fondamentales

Disciplines :

Physics

Author, co-author :

Bergshoeff, Eric A.; University of Groningen

CAMPOLEONI, Andrea ; Université de Mons - UMONS > Faculté des Sciences > Service de Physique de l'Univers, Champs et Gravitation

Fontanella, Andrea; Perimeter Institute ; Trinity College Dublin

Mele, Lea ; Université de Mons - UMONS > Faculté des Sciences > Service de Physique de l'Univers, Champs et Gravitation

Rosseel, Jan; Rudjer Boskovic Institute

Language :

English

Title :

Carroll fermions

Publication date :

14 June 2024

Journal title :

SciPost Physics

eISSN :

2542-4653

Publisher :

Stichting SciPost

Volume :

Issue :

Pages :

153

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://scipost.org/10.21468/SciPostPhys.16.6.153/pdf

Research unit :

S827 - Physique de l'Univers, Champs et Gravitation

Research institute :

R150 - Institut de Recherche sur les Systèmes Complexes

Name of the research project :

4907 - MIS-Campoleoni - HighSpinSymm - Fédération Wallonie Bruxelles

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique

Funding number :

FC.55077; F.4503.20; T.0047.24

Available on ORBi UMONS :

since 17 June 2024

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Bibliography

J.-M. Lévy-Leblond, Une nouvelle limite non-relativiste du groupe de Poincaré, Ann. Inst. Henri Poincaré A Phys. Théor. 3, 1 (1965).
N. D. Sen Gupta, On an analogue of the Galilei group, Nuovo Cimento A 44, 512 (1966), doi:10.1007/BF02740871.
S. Pasterski, M. Pate and A.-M. Raclariu, Celestial holography, (arXiv preprint) doi:10.48550/arXiv.2111.11392.
L. Donnay, Celestial holography: An asymptotic symmetry perspective, Phys. Rep. 1073, 1 (2024), doi:10.1016/j.physrep.2024.04.003.
L. Donnay and C. Marteau, Carrollian physics at the black hole horizon, Class. Quantum Gravity 36, 165002 (2019), doi:10.1088/1361-6382/ab2fd5.
C. Duval, G. W. Gibbons and P. A. Horvathy, Conformal Carroll groups and BMS symmetry, Class. Quantum Gravity 31, 092001 (2014), doi:10.1088/0264-9381/31/9/092001.
A. Bagchi, S. Chakrabortty and P. Parekh, Tensionless strings from worldsheet symmetries, J. High Energy Phys. 01, 158 (2016), doi:10.1007/JHEP01(2016)158.
E. Casali and P. Tourkine, On the null origin of the ambitwistor string, J. High Energy Phys. 11, 036 (2016), doi:10.1007/JHEP11(2016)036.
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. Quantum Gravity 31, 085016 (2014), doi:10.1088/0264-9381/31/8/085016.
E. Bergshoeff, J. Gomis and G. Longhi, Dynamics of Carroll particles, Class. Quantum Gravity 31, 205009 (2014), doi:10.1088/0264-9381/31/20/205009.
A. Bagchi, A. Mehra and P. Nandi, Field theories with conformal Carrollian symmetry, J. High Energy Phys. 05, 108 (2019), doi:10.1007/JHEP05(2019)108.
M. Henneaux and P. Salgado-Rebolledo, Carroll contractions of Lorentz-invariant theories, J. High Energy Phys. 11, 180 (2021), doi:10.1007/JHEP11(2021)180.
J. de Boer, J. Hartong, N. A. Obers, W. Sybesma and S. Vandoren, Carroll symmetry, dark energy and inflation, Front. Phys. 10, 810405 (2022), doi:10.3389/fphy.2022.810405.
B. Chen, R. Liu and Y.-f. Zheng, On higher-dimensional Carrollian and Galilean conformal field theories, SciPost Phys. 14, 088 (2023), doi:10.21468/SciPostPhys.14.5.088.
A. Bagchi, D. Grumiller and P. Nandi, Carrollian superconformal theories and super BMS, J. High Energy Phys. 05, 044 (2022), doi:10.1007/JHEP05(2022)044.
D. Rivera-Betancour and M. Vilatte, Revisiting the Carrollian scalar field, Phys. Rev. D 106, 085004 (2022), doi:10.1103/PhysRevD.106.085004.
S. Baiguera, G. Oling, W. Sybesma and B. T. Søgaard, Conformal Carroll scalars with boosts, SciPost Phys. 14, 086 (2023), doi:10.21468/SciPostPhys.14.4.086.
A. Banerjee, S. Dutta and S. Mondal, Carroll fermions in two dimensions, Phys. Rev. D 107, 125020 (2023), doi:10.1103/PhysRevD.107.125020.
A. Bagchi, A. Banerjee, R. Basu, M. Islam and S. Mondal, Magic fermions: Carroll and flat bands, J. High Energy Phys. 03, 227 (2023), doi:10.1007/JHEP03(2023)227.
X. Bekaert, A. Campoleoni and S. Pekar, Carrollian conformal scalar as flat-space singleton, Phys. Lett. B 838, 137734 (2023), doi:10.1016/j.physletb.2023.137734.
B. Chen, R. Liu, H. Sun and Y.-f. Zheng, Constructing Carrollian field theories from null reduction, J. High Energy Phys. 11, 170 (2023), doi:10.1007/JHEP11(2023)170.
K. Banerjee, R. Basu, B. Krishnan, S. Maulik, A. Mehra and A. Ray, One-loop quantum effects in Carroll scalars, Phys. Rev. D 108, 085022 (2023), doi:10.1103/PhysRevD.108.085022.
J. de Boer, J. Hartong, N. A. Obers, W. Sybesma and S. Vandoren, Carroll stories, J. High Energy Phys. 09, 148 (2023), doi:10.1007/JHEP09(2023)148.
K. Koutrolikos and M. Najafizadeh, Super-Carrollian and super-Galilean field theories, Phys. Rev. D 108, 125014 (2023), doi:10.1103/PhysRevD.108.125014.
O. Kasikci, M. Ozkan, Y. Pang and U. Zorba, Carrollian supersymmetry and SYK-like models, (arXiv preprint) doi:10.48550/arXiv.2311.00039.
L. Ciambelli, Dynamics of Carrollian scalar fields, (arXiv preprint) doi:10.48550/arXiv.2311.04113.
E. Bergshoeff, J. Figueroa-O’Farrill and J. Gomis, A non-lorentzian primer, SciPost Phys. Lect. Notes 69 (2023), doi:10.21468/SciPostPhysLectNotes.69.
M. B. Stakenborg, Carroll limit of the Dirac Lagrangian, MSc thesis, Universiteit Utrecht, Utrecht, Netherlands (2023).
H. C. Lee, On Clifford algebras and their representations, Ann. Math. 49, 760 (1948), doi:10.2307/1969398.
J. A. Brooke, A Galileian formulation of spin. I. Clifford algebras and spin groups, J. Math. Phys. 19, 952 (1978), doi:10.1063/1.523798.
J. A. Brooke, A Galileian formulation of spin. II. Explicit realizations, J. Math. Phys. 21, 617 (1980), doi:10.1063/1.524506.
L. Mele, Carrollian fermions coupled to gravity, MSc thesis, Université de Mons, Mons, Belgium (2023).
P.-x. Hao, W. Song, X. Xie and Y. Zhong, BMS-invariant free scalar model, Phys. Rev. D 105, 125005 (2022), doi:10.1103/PhysRevD.105.125005.
A. Bagchi, A. Banerjee, S. Dutta, K. S. Kolekar and P. Sharma, Carroll covariant scalar fields in two dimensions, J. High Energy Phys. 01, 072 (2023), doi:10.1007/JHEP01(2023)072.
L. Bidussi, J. Hartong, E. Have, J. Musaeus and S. Prohazka, Fractons, dipole symmetries and curved spacetime, SciPost Phys. 12, 205 (2022), doi:10.21468/SciPostPhys.12.6.205.
O. Kasikci, M. Ozkan and Y. Pang, Carrollian origin of spacetime subsystem symmetry, Phys. Rev. D 108, 045020 (2023), doi:10.1103/PhysRevD.108.045020.
E. Bergshoeff, J. Gomis, B. Rollier, J. Rosseel and T. ter Veldhuis, Carroll versus Galilei gravity, J. High Energy Phys. 03, 165 (2017), doi:10.1007/JHEP03(2017)165.
E. A. Bergshoeff, J. M. Figueroa-O’Farrill, K. S. van Helden, J. Rosseel, I. J. Rotko and T. ter Veldhuis, p-brane Galilean and Carrollian geometries and gravities, J. Phys. A: Math. Theor. 57, 245205 (2024), doi:10.1088/1751-8121/ad4c62.
A. Barducci, R. Casalbuoni and J. Gomis, Confined dynamical systems with Carroll and Galilei symmetries, Phys. Rev. D 98, 085018 (2018), doi:10.1103/PhysRevD.98.085018.
E. Bergshoeff, J. M. Izquierdo and L. Romano, Carroll versus Galilei from a brane perspective, J. High Energy Phys. 10, 066 (2020), doi:10.1007/JHEP10(2020)066.
J. Figueroa-O’Farrill, E. Have, S. Prohazka and J. Salzer, The gauging procedure and carrollian gravity, J. High Energy Phys. 09, 243 (2022), doi:10.1007/JHEP09(2022)243.
A. Campoleoni, M. Henneaux, S. Pekar, A. Pérez and P. Salgado-Rebolledo, Magnetic Carrollian gravity from the Carroll algebra, J. High Energy Phys. 09, 127 (2022), doi:10.1007/JHEP09(2022)127.
M. Henneaux, Geometry of zero signature space-times, Bull. Soc. Math. Belg. 31, 47 (1979).
J. Hartong, Gauging the Carroll algebra and ultra-relativistic gravity, J. High Energy Phys. 08, 069 (2015), doi:10.1007/JHEP08(2015)069.
D. Hansen, N. Obers, G. Oling and B. T. Søgaard, Carroll expansion of general relativity, SciPost Phys. 13, 055 (2022), doi:10.21468/SciPostPhys.13.3.055.
C. Batlle, J. Gomis, L. Mezincescu and P. K. Townsend, Tachyons in the Galilean limit, J. High Energy Phys. 04, 120 (2017), doi:10.1007/JHEP04(2017)120.
J. Gomis, K. Kamimura and P. K. Townsend, Non-relativistic superbranes, J. High Energy Phys. 11, 051 (2004), doi:10.1088/1126-6708/2004/11/051.
C. N. Pope, Lectures on W algebras and W gravity, in High energy physics and cosmology: Proceedings of the 1991 summer school, World Scientific, Singapore, ISBN 9789814554725 (1992), doi:10.1142/1699.
E. Bergshoeff, B. de Wit and M. Vasiliev, The structure of the super-W∞(λ) algebra, Nucl. Phys. B 366, 315 (1991), doi:10.1016/0550-3213(91)90005-I.
E. Bergshoeff, A. Fontanella and J. Rosseel, In preparation.