arXiv subjects

Antonino Flachi

Publications and source records attributed to Antonino Flachi.

At least 37 records · Page 2Linked to original sources

arXiv2018

Symmetry Breaking and Lattice Kirigami

In this work 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 non-vanishing 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 non-dynamical 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 behaviour 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.

hep-th↗

arXiv2018

Quantum vacuum polarization around a Reissner-Nordström black hole in five dimensions

WKB approximation methods are applied to the case of a massive scalar field around a 5-dimensional Reissner-Nordström black hole. The divergences are explicitly isolated and the cancellation against the Schwinger-De Witt counter-terms 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.

gr-qc↗

arXiv2017

Sign Flip in the Casimir Force for Interacting Fermion Systems

In this work we consider a fermionic chain of finite length $\ell$. Fermions are allowed to interact and are forced to obey boundary conditions, thus altering the process of condensation. Our goal is to explore how this affects the quantum vacuum energy for this system. We approach this problem by using a self-consistent method and observe a nontrivial behavior in the Casimir force, displaying a switch from an attractive to a repulsive regime. This flip stems from the competition between the attractive contribution from the usual fermionic Casimir effect and a repulsive one coming from the condensate.

hep-th↗

arXiv2016

Black Hole Quantum Vacuum Polarization in Higher Dimensions

The goal of this paper is to extend to higher dimensionality the methods and computations of vacuum polarization effects in black hole spacetimes. We focus our attention on the case of five dimensional Schwarzschild-Tangherlini black holes, for which we adapt the general method initially developed by Candelas and later refined by Anderson and others. We make use of point splitting regularization and of the WKB approximation to extract the divergences occuring in the coincidence limit of the Green function and, after calculating the counter-terms using the Schwinger - De Witt expansion, we explicitly prove the cancellation of the divergences and the regularity of the vacuum polarization once counter-terms are added up. We finally handle numerically the renormalized expression of the vacuum polarization. As a check on the method we also prove the regularity of the vacuum polarization in the six dimensional case in the large mass limit.

gr-qc↗

arXiv2016

Vacuum polarization in asymptotically Lifshitz black holes

There has been considerable interest in applying the gauge/gravity duality to condensed matter theories with particular attention being devoted to gravity duals (Lifshitz spacetimes) of theories that exhibit anisotropic scaling. In this context, black hole solutions with Lifshitz asymptotics have also been constructed aiming at incorporating finite temperature effects. The goal here is to look at quantum polarization effects in these spacetimes, and to this aim, we develop a way to compute the coincidence limit of the Green's function for massive, non-minimally coupled scalar fields, adapting to the present situation the analysis developed for the case of asymptotically anti de Sitter black holes. The basics are similar to previous calculations, however in the Lifshitz case one needs to extend previous results to include a more general form for the metric and dependence on the dynamical exponent. All formulae are shown to reduce to the AdS case studied before once the value of the dynamical exponent is set to unity and the metric functions are accordingly chosen. The analytical results we present are general and can be applied to a variety of cases, in fact, to all spherically symmetric Lifshitz black hole solutions. We also implement the numerical analysis choosing some known Lifshitz black hole solutions as illustration.

gr-qc↗

arXiv2015

Bubble-wall Casimir interaction in fermionic environments

We consider the Casimir interaction, mediated by massless fermions, between a spherical defect and a flat potential barrier, assuming hard (bag-type) boundary conditions at both the barrier and the surface of the sphere. The computation of the quantum interaction energy is carried out using the multiple scattering approach, adapted here to the setup in question. We find an exact integral formula for the energy, from which we extract both the large and short distance asymptotic behaviour. At large distance the fermionic contribution is found to scale as $L^{-3}$, in contrast to that of electromagnetic vacuum fluctuations that, assuming perfectly conducting boundaries, scales as $L^{-4}$. At short distance, we compute the leading and sub-leading contribution to the vacuum energy. The leading one coincides with what it is expected from the proximity force approximation, while the sub-leading term gives, contrary to the electromagnetic case, a positive correction to the proximity force result.

hep-th↗

arXiv2015

Chiral gap effect in curved space

We discuss a new type of QCD phenomenon induced in curved space. In the QCD vacuum, a mass-gap of Dirac fermions is attributed to the spontaneous breaking of chiral symmetry. If the curvature is positive large, the chiral condensate melts but a chiral invariant mass-gap can still remain, which we name the chiral gap effect in curved space. This leads to decoupling of quark deconfinement which implies a view of black holes surrounded by a first-order QCD phase transition.

hep-th↗

arXiv2015

Geometrically induced magnetic catalysis and critical dimensions

We discuss the combined effect of magnetic fields and geometry in interacting fermionic systems. At leading order in the heat-kernel expansion, the infrared singularity (that in flat space leads to the magnetic catalysis) is regulated by the chiral gap effect, and the catalysis is deactivated by the effect of the scalar curvature. We discover that an infrared singularity is found in higher-order terms that mix the magnetic field with curvature, and these lead to a novel form of geometrically induced magnetic catalysis. The dynamical mass squared is then modified not only due to the chiral gap effect by an amount proportional to the curvature, but also by a magnetic shift $\propto (4-D)eB$, where $D$ represents the number of space-time dimensions. We argue that $D=4$ is a critical dimension across which the behavior of the magnetic shift changes qualitatively.

hep-th↗

arXiv2013

Dual Fermion Condensates in Curved Space

In this paper we compute the effective action at finite temperature and density for the dual fermion condensate in curved space with the fermions described by an effective field theory with four-point interactions. The approach we adopt refines a technique developed earlier to study chiral symmetry breaking in curved space and it is generalized here to include the U$(1)$-valued boundary conditions necessary to define the dual condensate. The method we present is general, includes the coupling between the fermion condensate and the Polyakov loop, and applies to any ultrastatic background spacetime with a nonsingular base. It also allows one to include inhomogeneous and anisotropic phases and therefore it is suitable to study situations where the geometry is not homogeneous. We first illustrate a procedure, based on heat kernels, useful to deal with situations where the dual and chiral condensates (as well as any smooth background field eventually present) are slowly or rapidly varying functions in space. Then we discuss a different approach based on the density of states method and on the use of Tauberian theorems to handle the case of arbitrary chemical potentials. As a trial application, we consider the case of constant curvature spacetimes and show how to compute numerically the dual fermion condensate in the case of both homogeneous and inhomogeneous phases.

hep-th↗

arXiv2013

Moduli Stabilization in a de Sitter Compactification Model

We discuss the moduli stabilization in a de Sitter compactification model obtained coupling D-dimensional gravity to scalar and gauge fields. This class of models is characterized by two moduli: one related to the volume of the internal space, the other to the warp factor. While the volume modulus can be fixed by appropriately tuning the gauge field strength, curvature of the internal space, and cosmological constant, the same mechanism does not work for the warp modulus. In this paper we discuss a stabilization mechanism based on quantum effects and show that both moduli can be efficiently stabilized.

hep-th↗

arXiv2013

Deconfinement transition and Black Holes

In this paper we propose an effective description of the transition to deconfinement in the vicinity of a black hole. For this we adapt the approach that uses the dual quark condensate as order parameter for confinement, originally introduced in the context of lattice QCD, to a strongly interacting fermion effective field theory propagating on a curved background. We construct numerically the dual condensate and determine approximately the region of the deconfined phase. The present analysis suggests that quarks will be radiated directly by Hawking emission, while hadrons will form at the boundary of the deconfined region by "standard" nonperturbative QCD effects. This example provides a nontrivial setup to discuss how gravity affects confinement.

hep-th↗

arXiv2013

Strongly Interacting Fermions and Phases of the Casimir Effect

With the intent of exploring how the interplay between boundary effects and chiral symmetry breaking may alter the thermodynamical behavior of a system of strongly interacting fermions, we study the Casimir effect for the setup of two parallel layers using a four-fermion effective field theory at zero density. This system reveals a number of interesting features. While for infinitely large separation (no boundaries), chiral symmetry is broken or restored via a second order phase transition, in the opposite case of small (and, in general, finite) separation the transition becomes first order, rendering effects of finite size, for the present setup, similar to those of a chemical potential. Appropriately moving on the separation-temperature plane, it is possible to generate a peculiar behavior in the temperature dependence of the thermodynamic potential and of the condensate, compensating thermal with geometrical variations. A behavior similar to what we find here has been predicted to occur in bilayer graphene. Chiral symmetry breaking induces different phases (massless and massive) in the Casimir force separated by critical lines.

hep-th↗

arXiv2013

Quasinormal modes of regular black holes

Black hole quasinormal frequencies are complex numbers that encode information on how a black hole relaxes after it has been perturbed and depend on the features of the geometry and on the type of perturbations. On the one hand, the examples studied so far in the literature focused on the case of black hole geometries with singularities in their interior. On the other hand, it is expected that quantum or classical modifications of general relativity may correct the pathological singular behavior of classical black hole solutions. Despite the fact that we do not have at hand a complete theory of quantum gravity, regular black hole solutions can be constructed by coupling gravity to an external form of matter, sometimes modeled by one form or another of nonlinear electrodynamics. It is therefore relevant to compute quasinormal frequencies for these regular solutions and see how differently, from the ordinary ones, regular black holes ring. In this paper, we take a step in this direction and, by computing the quasinormal frequencies, study the quasinormal modes of neutral and charged scalar field perturbations on regular black hole backgrounds in a variety of models.

gr-qc↗

arXiv2012

Interacting Fermions, Boundaries, and Finite Size Effects

In this work we analyze how effects of finite size may modify the thermodynamics of a system of strongly interacting fermions that we model using an effective field theory with four-point interactions at finite temperature and density and look in detail at the case of a confining two-layer system. We compute the thermodynamic potential in the large-$N$ and mean-field approximations and adopt a zeta-function regularization scheme to regulate the divergences. Explicit expansions are obtained in different regimes of temperature and separation. The analytic structure of the potential is carefully analyzed and relevant integral and series representations for the various expressions involved are obtained. Several known results are obtained as limiting case of general results. We numerically implement the formalism and compute the thermodynamic potential, the critical temperature and the fermion condensate showing that effects of finite size tend to shift the critical points and the order of the transitions. The present discussion may be of some relevance for the study of the Casimir effect between strongly coupled fermionic materials with inter-layer interactions.

hep-th↗

arXiv2011

Chiral Modulations in Curved Space II: Conifold Geometries

In this paper, we extend our previous analysis concerning the formation of inhomogeneous condensates in strongly-coupled fermion effective field theories on curved spaces and include the case of conifold geometries that represent the simplest tractable case of manifolds with curvature singularities. In the set-up considered here, by keeping the genuine thermodynamical temperature constant, we may single out the role that curvature effects play on the breaking/restoration of chiral symmetry and on the appearance of inhomogeneous phases. The first goal of this paper is to construct a general expression of the finite temperature effective action for inhomogeneous condensates in the case of four-fermion effective field theories on conifold geometries with generic Riemannian smooth base (generalised cones). The other goal is to implement numerically the above formal results and construct self-consistent solutions for the condensate. We explicitly show that the condensate assumes a kink-like profile, vanishing at the singularity that is surrounded by a bubble of restored chiral symmetry phase.

hep-th↗

arXiv2011

Chiral Phase Transitions around Black Holes

In this paper we discuss the possibility that chiral phase transitions, analogous to those of QCD, occur in the vicinity of a black hole. If the black hole is surrounded by a gas of strongly interacting particles, an inhomogeneous condensate will form. We demonstrate this by explicitly constructing self-consistent solutions.

hep-th↗

arXiv2011

Chiral Modulations in Curved Space I: Formalism

The goal of this paper is to present a formalism that allows to handle four-fermion effective theories at finite temperature and density in curved space. The formalism is based on the use of the effective action and zeta function regularization, supports the inclusion of inhomogeneous and anisotropic phases. One of the key points of the method is the use of a non-perturbative ansatz for the heat-kernel that returns the effective action in partially resummed form, providing a way to go beyond the approximations based on the Ginzburg-Landau expansion for the partition function. The effective action for the case of ultra-static Riemannian spacetimes with compact spatial section is discussed in general and a series representation, valid when the chemical potential satisfies a certain constraint, is derived. To see the formalism at work, we consider the case of static Einstein spaces at zero chemical potential. Although in this case we expect inhomogeneous phases to occur only as meta-stable states, the problem is complex enough and allows to illustrate how to implement numerical studies of inhomogeneous phases in curved space. Finally, we extend the formalism to include arbitrary chemical potentials and obtain the analytical continuation of the effective action in curved space.

hep-th↗

arXiv2010

Zeta Determinant for Laplace Operators on Riemann Caps

The goal of this paper is to compute the zeta function determinant for the massive Laplacian on Riemann caps (or spherical suspensions). These manifolds are defined as compact and boundaryless $D-$dimensional manifolds deformed by a singular Riemannian structure. The deformed spheres, considered previously in the literature, belong to this class. After presenting the geometry and discussing the spectrum of the Laplacian, we illustrate a method to compute its zeta regularized determinant. The special case of the deformed sphere is recovered as a limit of our general formulas.

math-ph↗