論文

© 2019 In this work, we derive exact self-consistent solutions to the gap equations of the CPN−1 model on a finite interval with Dirichlet boundary conditions in the large-N approximation. The solution reproduces the confining phase in the infinite system by taking the appropriate limit. We compute the vacuum energy and the Casimir force and observe that the sign of the force is always attractive.

© 2018 authors. Published by the American Physical Society. We perform an explicit calculation of the axial current at finite rotation and temperature in curved space. We find that finite curvature and mass corrections to the chiral vortical effect satisfy a relation of the chiral gap effect, that is, a fermion mass shift by a scalar curvature. We also point out that a product term of the angular velocity and the scalar curvature shares the same coefficient as the mixed gravitational chiral anomaly. We discuss possible applications of the curvature-induced chiral vortical effect to rotating astrophysical compact objects described by the Kerr metric. Instead of direct calculation, we assume that the Chern-Simons current can approximate the physical axial current. We make a proposal that the chiral vortical current from rotating compact objects could provide a novel microscopic mechanism behind the generation of collimated jets.

© Published under licence by IOP Publishing Ltd. External conditions have a dramatic impact on the way dynamical symmetry breaking occurs. In a curved background, the natural expectation is that curvature works toward the restoration of the internal symmetry. We show instead that, for topological defects, the competing action of the locally induced curvature and boundary conditions generated by the non-trivial topology allows configurations where symmetries can be spontaneously broken close to the core. Inspired by the effect of geometrical deformations on 2D lattices, we then propose a novel mechanism to induce a superconducting phase by triggering condensation along cosmic strings.

© 2019 authors. Published by the American Physical Society. In this work we examine a system consisting of a confined one-dimensional arrangement of atoms that we describe by using the 2-dimensional CPN-1 model, restricted to an interval and at finite temperature. We develop a method to obtain the bulk and boundary parts of the one-loop effective action as a function of the effective mass of the fluctuations. The formalism has the advantage of allowing for a systematic analysis of a large class of boundary conditions and to model the (adiabatic) response of the ground state to changes in the boundary conditions. In the case of periodic boundary conditions, we find that inhomogeneous phases are disfavored for intervals of large size. Away from periodic boundary conditions, our numerical results show that the ground state has a generic crystal-like structure that can be modulated by variations of the boundary conditions. The results presented here could be relevant for experimental implementations of nonlinear sigma models and could be tested by lattice numerical simulations.

Copyright © 2018 by the Editors.All rights reserved. In this work we summarize our computation of the vacuum polarization for a massive non-minimally coupled scalar field on a Lifshitz black hole background. The general method for computing the Green function is outlined and a procedure to renormalize is described We also provide numerical results for some specific values of mass, nonminimal coupling, and dynamical exponent.

© 2018 American Physical Society. WKB approximation methods are applied to the case of a massive scalar field around a five-dimensional Reissner-Nordström black hole. The divergences are explicitly isolated, and the cancellation against the Schwinger-DeWitt counterterms are proven. The resulting finite quantity is evaluated for different values of the free parameters, namely, the black hole mass and charge, and the scalar field mass. We thus extend our previous results on quantum vacuum polarization effects for uncharged asymptotically flat higher-dimensional black holes to electrically charged black holes.

In this paper we consider the ${\mathbb C}P^{N-1}$ model confined to an interval of finite size at finite temperature and chemical potential. We compute, in the large-$N$ approximation, the one-loop effective action of the order parameter associated with the effective mass of the quantum fluctuations. To discuss some generic features of the ground state of the model, we work out a mixed-gradient expansion and obtain an expression for the thermodynamic potential density as a functional of the order parameter, generalizing previous calculations to arbitrarily large order and to the case of small finite density. The technique used here relies on analytic regularization and provides an efficient scheme to extract the coefficients of the expansion. These coefficients are then used to deduce some generic properties of the ground state as a function of external conditions. For vanishing chemical potential and intervals of any size, we show that inhomogeneous phases are not energetically favored, but we find evidence that they may become energetically favored for large enough values of the chemical potential. We also show that there can be no transition to a massless phase for any value of the external conditions and clarify a seemingly important point regarding the regularization of the effective action connected to the appearance of logarithmic divergences and to the Mermin-Wagner-Hoenberg-Coleman theorem.

© 2019, The Author(s). We consider the restoration of a spontaneously broken symmetry of an interacting quantum scalar field around neutral, i.e., Schwarzschild, and electrically charged, i.e., Reissner-Nordström, black holes in four dimensions. This is done through a semi-classical self-consistent procedure, by solving the system of non-linear coupled equations describing the dynamics of the background field and the vacuum polarization. The black hole at its own horizon generates an indefinitely high temperature which decreases to the Hawking temperature at infinity. Due to the high temperature in its vicinity, there forms a bubble around the black hole in which the scalar field can only assume a value equal to zero, a minimum of energy. Thus, in this region the symmetry of the energy and the field is preserved. At the bubble radius, there is a phase transition in the value of the scalar field due to a spontaneous symmetry breaking mechanism. Indeed, outside the bubble radius the temperature is low enough such that the scalar field settles with a nonzero value in a new energy minimum, indicating a breaking of the symmetry in this outer region. Conversely, there is symmetry restoration from the outer region to the inner bubble close to the horizon. Specific properties that emerge from different black hole electric charges are also noteworthy. It is found that colder black holes, i.e., more charged ones, have a smaller bubble length of restored symmetry. In the extremal case the bubble has zero length, i.e., there is no bubble. Additionally, for colder black holes, it becomes harder to excite the quantum field modes, so the vacuum polarization has smaller values. In the extremal case, the black hole temperature is zero and the vacuum polarization is never excited.

© 2018 authors. Published by the American Physical Society. We consider an interacting quantum field theory on a curved two-dimensional manifold that we construct by geometrically deforming a flat hexagonal lattice by the insertion of a defect. Depending on how the deformation is done, the resulting geometry acquires a locally nonvanishing curvature that can be either positive or negative. Fields propagating on this background are forced to satisfy boundary conditions modulated by the geometry and that can be assimilated by a nondynamical gauge field. We present an explicit example where curvature and boundary conditions compete in altering the way symmetry breaking takes place, resulting in a surprising behavior of the order parameter in the vicinity of the defect. The effect described here is expected to be generic and of relevance in a variety of situations.

© 2019 authors. Published by the American Physical Society. Recent work has analyzed how deformations due to the insertion of a defect in a flat hexagonal lattice affect the ground state structure of an interacting fermion field theory. Such modifications result in an increase of the order parameter in the vicinity of the defect and can be explained by a kirigami effect, that is the combined effect of the curvature, locally introduced by the deformation in the lattice tessellation, and of a synthetic gauge field induced by the boundary conditions along the cut, performed to introduce the defect. In this work, we extend the formalism and previous results to include finite temperature effects.