Abstract
We consider sets of states in conformal quantum mechanics associated to generators of time evolution whose orbits cover different regions of the time domain. States labelled by a continuous global time variable define the two-point correlation functions of the theory seen as a one-dimensional conformal field theory. Such states exhibit the structure of a thermofield double built on bipartite eigenstates of generators of non-global time evolution. In terms of the correspondence between radial conformal symmetries in Minkowski space-time and time evolution in conformal quantum mechanics proposed in [1, 2] these generators coincide with conformal Killing vectors tangent to worldlines of Milne and diamond observers at constant radius. The temperature of the thermofield double states in conformal quantum mechanics reproduces the temperatures perceived by such diamond and Milne observers. We calculate the entanglement entropy associated to the thermofield double states and obtain a UV divergent logarithmic behaviour analogous to known results in two-dimensional conformal field theory in which the entangling boundary is point-like.
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Acknowledgments
We acknowledge support from the INFN Iniziativa Specifica QUAGRAP. This research was carried out in the frame of Programme STAR Plus, financially supported by the University of Napoli Federico II and Compagnia di San Paolo. This work also falls within the scopes of the European Union COST Action CA18108 Quantum gravity phenomenology in the multi-messenger approach.
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Arzano, M., D’Alise, A. & Frattulillo, D. Entanglement entropy in conformal quantum mechanics. J. High Energ. Phys. 2023, 165 (2023). https://doi.org/10.1007/JHEP10(2023)165
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DOI: https://doi.org/10.1007/JHEP10(2023)165