Entanglement Entropy and Quantum Phase Transition in the O(N) σ-model

We investigate how entanglement entropy behaves in a non-conformal scalar field system with a quantum phase transition, by the replica method. We study the σ-model in 3+1 dimensions which is O(N) symmetric as the mass squared parameter μ2 is positive, and undergoes spontaneous symmetry breaking while μ2 becomes negative. The area law leading divergence of the entanglement entropy is preserved in both of the symmetric and the broken phases. The spontaneous symmetry breaking changes the subleading divergence from log to log squared, due to the cubic interaction on the cone. At the leading order of the coupling constant expansion, the entanglement entropy reaches a cusped maximum at the quantum phase transition point μ2 = 0, and decreases while μ2 is tuned away from 0 into either phase.

Static Casimir condensate of conformal scalar field in Friedmann universe

The quantum Casimir condensate of a conformal massive scalar field in a compact Friedmann universe is considered in the static approximation. The Abel–Plana formula is used for renormalization of divergent series in the condensate calculation. A differential relation between the static Casimir energy density and static Casimir condensate is derived.

The Bekenstein-Hawking Corpuscular Cascading from the Back-Reacted Black Hole

Exciting peculiarities of Planck-scale physics have immediate effects on the Bekenstein-Hawking radiation emitted from black holes (BHs). In this paper, using the tunneling formalism, we determine the Bekenstein-Hawking temperature for the vector particles from a back-reacted black hole (BBH) constructed from a conformal scalar field surrounded by a BTZ (Banados-Teitelboim-Zanelli) BH. Then, under the effect of the generalized uncertainty principle, we extend our calculations for scalar particles to understand the effects of quantum gravity. Then, we calculate an evaporation time for the BBH, the total number of Bekenstein-Hawking particles, and the quantum corrections of the number. We observe that remnants of the BH evaporation occur and that they affect the Bekenstein-Hawking temperature of the BBH as well as the total number of Bekenstein-Hawking particles.

Higgs-like field from extended theory of gravitation

We shall consider possible potentials emerging in (purely metric) f(R)-theories for the conformal scalar field. We shall discuss possible approaches to determine models with specific potentials and show that some potentials qualitatively similar to the typical Higgs potentials are allowed.