PoS - Proceedings of Science
Volume 463 - Corfu Summer Institute 2023 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2023) - Workshop on Noncommutative and Generalized Geometry in String Theory, Gauge Theory and Related Physical Models
Entanglement entropy and horizon temperature in conformal quantum mechanics
M. Arzano*, A. D’Alise and D. Frattulillo
Full text: pdf
Published on: July 31, 2024
Abstract
The generators of radial conformal symmetries in Minkowski space-time can be put in correspondence with generators of time evolution in conformal quantum mechanics. Within this correspondence we show that in conformal quantum mechanics the state corresponding to the inertial vacuum for a conformally invariant field in Minkowski spacetime has the structure of a thermofield double. The latter is built from a bipartite ”vacuum state” corresponding to the ground state of the generators of hyperbolic time evolution. These can evolve states only within a portion of the time domain. When such generators correspond to conformal Killing vectors mapping a causal diamond in itself and generators of dilations, the temperature of the thermofield double reproduces, respectively, the diamond temperature and the Milne temperature found for massless fields in Minkowski spacetime. Moreover 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.
DOI: https://doi.org/10.22323/1.463.0276
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