Abstract
We study various aspects of the Carroll limit in which the speed of light is sent to zero. A large part of this paper is devoted to the quantization of Carroll field theories. We show that these exhibit infinite degeneracies in the spectrum and may suffer from non-normalizable ground states. As a consequence, partition functions of Carroll systems are ill-defined and do not lead to sensible thermodynamics. These seemingly pathological properties might actually be a virtue in the context of flat space holography.
Better defined is the Carroll regime, in which we consider the leading order term in an expansion around vanishing speed of light without taking the strict Carroll limit. Such an expansion may lead to sensible notions of Carroll thermodynamics. An interesting example is a gas of massless particles with an imaginary chemical potential conjugate to the momentum. In the Carroll regime we show that the partition function of such a gas leads to an equation of state with w = −1.
As a separate story, we study aspects of Carroll gravity and couplings to Carrollian energy-momentum tensors. We discuss many examples of solutions to Carroll gravity, including wormholes, Maxwell fields, solutions with a cosmological constant, and discuss the structure of geodesics in a Carroll geometry. The coupling of matter to Carroll gravity also allows us to derive energy-momentum tensors for hypothetical Carroll fluids from expanding relativistic fluids as well as directly from hydrostatic partition functions.
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Acknowledgments
It is a pleasure to thank the organizers and participants of the workshops on Carrollian and Non-Lorentzian Geometry in Vienna, Mons and Edinburgh, where some of these results were presented. In particular we thank Arjun Bagchi, Eric Bergshoeff, Laura Donnay, Daniel Grumiller, Marc Henneaux, Gerben Oling, Simon Pekar and Marios Petropoulos for useful discussions. JdB is supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013), ERC Grant agreement ADG 834878. JH is supported by the Royal Society University Research Fellowship Renewal “Non-Lorentzian String Theory” (grant number URF\R\221038). The work of NO is supported in part by VR project grant 2021-04013 and Villum Foundation Experiment project 00050317, “Exploring the wonderland of Carrollian physics: Extreme gravity, spacetime horizons and supersonic fluids”. Nordita is supported in part by Nordforsk. WS is supported by the Icelandic Research Fund via the Grant of Excellence titled “Quantum Fields and Quantum Geometry” and by the University of Iceland Research Fund.
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de Boer, J., Hartong, J., Obers, N.A. et al. Carroll stories. J. High Energ. Phys. 2023, 148 (2023). https://doi.org/10.1007/JHEP09(2023)148
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DOI: https://doi.org/10.1007/JHEP09(2023)148