Abstract
At extreme energies, both low and high, the spacetime symmetries of relativistic quantum field theories (QFTs) are expected to change with Galilean symmetries emerging in the very low energy domain and, as we will argue, Carrollian symmetries appearing at very high energies. The formulation of Wilsonian renormalisation group seems inadequate for handling these changes of the underlying Poincare symmetry of QFTs and it seems unlikely that these drastic changes can be seen within the realms of relativistic QFT. We show that contrary to this expectation, changes in the spacetime algebra occurs at the very edges of parameter space. In particular, we focus on the very high energy sector and show how bilinears of U(1) currents added to a two dimensional (massless) scalar field theory deform the relativistic spacetime conformal algebra to conformal Carroll as the effective coupling of the deformation is dialed to infinity. We demonstrate this using both a symmetric and an antisymmetric current-current deformation for theories with multiple scalar fields. These two operators generate distinct kinds of quantum flows in the coupling space, the symmetric driven by Bogoliubov transformations and the antisymmetric by spectral flows, both leading to Carrollian CFTs at the end of the flow.
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Acknowledgments
The authors would like to thank Rudranil Basu, Joydeep Chakrabortty, Ritankar Chatterjee, Stephane Detourney, Priyadarshini Pandit and especially Shahin Sheikh-Jabbari for many fruitful discussions.
AB is partially supported by a Swarnajayanti Fellowship of the Department of Science and Technology and Science and Engineering Research Board (SERB) and also by the following SERB grants SB/SJF/2019-20/08, CRG/2022/006165. ArB is supported in part by an OPERA grant and a seed grant NFSG/PIL/2023/P3816 from BITS-Pilani. ArB would like to thank Kyoto University, TU Wien, CNRS Paris and IIT Kanpur for kind hospitality during the various stages of this work. SM is supported by grant number 09/092(1039)/2019-EMR-I from Council of Scientific and Industrial Research (CSIR). DM is supported by a Young Scientist Training Program (YST) Fellowship from Asia Pacific Center for Theoretical Physics (APCTP). The work of HM is supported by the Institute for Basic Science (IBS-R003-D1).
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Bagchi, A., Banerjee, A., Mondal, S. et al. Beyond Wilson? Carroll from current deformations. J. High Energ. Phys. 2024, 215 (2024). https://doi.org/10.1007/JHEP06(2024)215
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DOI: https://doi.org/10.1007/JHEP06(2024)215