Entanglement entropy and horizon temperature in conformal quantum mechanics
arxiv(2024)
摘要
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 space-time 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 space-time. Moreover, we compute the entanglement
entropy associated to the thermofield double states obtaining a UV divergent
logarithmic behaviour akin to known results in two-dimensional conformal field
theory where the entangling boundary is point-like.
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