arXiv subjects

Antonino Flachi

Publications and source records attributed to Antonino Flachi.

53 records · Page 3Linked to original sources

arXiv2010

A new scheme for the running coupling constant in gauge theories using Wilson loops

We propose a new renormalization scheme of the running coupling constant in general gauge theories using the Wilson loops. The renormalized coupling constant is obtained from the Creutz ratio in lattice simulations and the corresponding perturbative coefficient at the leading order. The latter can be calculated by adopting the zeta-function resummation techniques. We perform a benchmark test of our scheme in quenched QCD with the plaquette gauge action. The running of the coupling constant is determined by applying the step-scaling procedure. Using several methods to improve the statistical accuracy, we show that the running coupling constant can be determined in a wide range of energy scales with relatively small number of gauge configurations.

hep-lat↗

arXiv2009

Casimir Effect on the brane

We consider the Casimir effect between two parallel plates localized on a brane. In order to properly compute the contribution to the Casimir energy due to any higher dimensional field, it is necessary to take into account the localization properties of the KK modes. When no massless mode appears in the spectrum, the correction to the Casimir energy is exponentially suppressed. When a massless mode is present in the spectrum, the correction to the Casimir energy can be, in principle, sizeable. Here we illustrate a new method to compute the correction to the Casimir energy between two parallel plates, localized on a brane. The Casimir energy is suppressed by two factors: at lowest order in $\varepsilon$, the correction comes entirely from the massive mode and turns out to be exponentially suppressed; the next-to-leading order correction in $\varepsilon$ follows, instead, a power-law suppression due to the small wave function overlap of the zero-mode with matter confined on the visible brane. Generic comments on the constraints on new physics that may arise from Casimir force experiments are also made.

hep-th↗

arXiv2009

Curvature corrections and topology change transition in brane-black hole systems: A perturbative approach

We consider curvature corrections to static, axisymmetric Dirac-Nambu-Goto membranes embedded into a spherically symmetric black hole spacetime with arbitrary number of dimensions. Since the next to leading order corrections in the effective brane action are quadratic in the brane thickness l, we adopt a linear perturbation approach in l^2. The perturbations are general in the sense that they are not restricted to the Rindler zone nor to the near-critical solutions of the unperturbed system. As a result, an unexpected asymmetry in the perturbed system is found. In configurations, where the brane does not cross the black hole horizon, the perturbative approach does not lead to regular solutions if the number of the brane's spacetime dimensions D>3. This condition, however, does not hold for the horizon crossing solutions. Consequently we argue that the presented perturbative approach breaks down for subcritical type solutions near the axis of the system for D>3. Nevertheless, we can discuss topology-changing phase transitions in cases when D=2 or 3, i.e. when the brane is a 1-dimensional string or a 2-dimensional sheet, respectively. For the general case, a different, non-perturbative approach should be sought. Based on the energy properties of those branes that are quasi-statically evolved from the equatorial configuration, we illustrate the results of the phase transition in the case of a D=3 brane. It is found that small thickness perturbations do not modify the order of the transition, i.e. it remains first order just as in the case of vanishing thickness.

gr-qc↗

arXiv2009

Quantum Back Reaction to asymptotically AdS Black Holes

We analyze the effects of the back reaction due to a conformal field theory (CFT) on a black hole spacetime with negative cosmological constant. We study the geometry numerically obtained by taking into account the energy momentum tensor of CFT approximated by a radiation fluid. We find a sequence of configurations without a horizon in thermal equilibrium (CFT stars), followed by a sequence of configurations with a horizon. We discuss the thermodynamic properties of the system and how back reaction effects alter the space-time structure. We also provide an interpretation of the above sequence of solutions in terms of the AdS/CFT correspondence. The dual five-dimensional description is given by the Karch-Randall model, in which a sequence of five-dimensional floating black holes followed by a sequence of brane localized black holes correspond to the above solutions.

gr-qc↗

arXiv2009

Search for the IR fixed point in the twisted Polyakov loop scheme

We present a non-perturbative study of the running coupling constant in the Twisted Polyakov Loop (TPL) scheme. We investigate how the systematic and statistical errors can be controlled {\it via} a feasibility study in SU(3) pure Yang-Mills theory. We show that our method reproduces the perturbative determination of the running coupling in the UV. In addition, our numerical result agrees with the theoretical prediction of this coupling constant in the IR. We also present our preliminary results for $N_f=12$ QCD, where an IR fixed point may be present.

hep-lat↗

arXiv2009

Field localization on a brane intersection in anti-de Sitter spacetime

We discuss the localization of scalar, fermion, and gauge field zero modes on a $3-$brane that resides at the intersection of two $4-$branes in six-dimensional anti-de Sitter space. This set-up has been introduced in the context of brane world models and, higher-dimensional versions of it, in string theory. In both six- and ten-dimensional cases, it has been shown that four-dimensional gravity can be reproduced at the intersection, due to the existence of a massless, localized graviton zero-mode. However, realistic scenarios require also the Standard Model to be localized on the $3-$brane. In this paper, we discuss under which conditions a higher-dimensional field theory, propagating on the above geometry, can have a zero-mode sector localized at the intersection and find that zero modes can be localized only if masses and couplings to the background curvature satisfy certain relations. We also consider the case when other 4-branes cut the bulk at some distance from the intersection and argue that, in the probe brane approximation, there is no significant effect on the localization properties at the $3-$brane. The case of bulk fermions is particularly interesting, since the properties of the geometry allow localization of chiral modes independently.

hep-th↗

arXiv2009

Spin Polarization Effects in Micro Black Hole Evaporation

We consider the evaporation of rotating micro black holes produced in highly energetic particle collisions, taking into account the polarization due to the coupling between the spin of the emitted particles and the angular momentum of the black hole. The effect of rotation shows up in the helicity dependent angular distribution significantly. By using this effect, there is a possibility to determine the axis of rotation for each black hole formed, suggesting a way to improve the statistics. Deviation from thermal spectrum is also a signature of rotation. This deviation is due to the fact that rapidly rotating holes have an effective temperature $T_{\rm eff}$ significantly higher than the Hawking temperature $T_H$. The deformation of the spectral shape becomes evident only for very rapidly rotating cases. We show that, since the spectrum follows a blackbody profile with an effective temperature, it is difficult to determine both the number of extra-dimensions and the rotation parameter from the energy spectrum alone. We argue that the helicity dependent angular distribution may provide a way to resolve this degeneracy. We illustrate the above results for the case of fermions.

hep-ph↗

arXiv2008

A New Method of Calculating the Running Coupling Constant

We propose a new method to compute the running coupling constant of gauge theories on the lattice. We first give the definition of the running coupling in the new scheme using the Wilson loops in a finite volume, and explain how the running of the coupling constant is extracted from the measurement of the volume dependence. The perturbative calculation of the renormalization constant to define the scheme is also given at the leading order. As a benchmark test of the new scheme we apply the method the case of the quenched QCD. We show the preliminary result from our numerical simulations which are carried out with plaquette gauge action for various lattice sizes and bare lattice couplings. With techniques to improve the statistical accuracy, we show that we can determine the non-perturbative running of the coupling constant in a wide range of the energy scale with relatively small number of gauge configurations in our scheme. We compare our lattice data of the running coupling constant with perturbative renormalization group evolution at one- and two-loop order, and confirm the consistency between them at high energy.

hep-lat↗

arXiv2008

Vacuum polarization in asymptotically anti-de Sitter black hole geometries

We study the polarization of the vacuum for a scalar field, $<ϕ^2 >$, on an asymptotically anti-de Sitter black hole geometry. The method we follow uses the WKB analytic expansion and point-splitting regularization, similarly to previous calculations in the asymptotically flat case. Following standard procedures, we write the Green function, regularize the initial divergent expression by point-splitting, renormalize it by subtracting geometrical counter-terms, and take the coincidence limit in the end. After explicitly demonstrating the cancellation of the divergences and the regularity of the Green function, we express the result as a sum of two parts. One is calculated analytically and the result expressed in terms of some generalized zeta-functions, which appear in the computation of functional determinants of Laplacians on Riemann spheres. We also describe some systematic methods to evaluate these functions numerically. Interestingly, the WKB approximation naturally organizes $<ϕ^2>$ as a series in such zeta-functions. We demonstrate this explicitly up to next-to-leading order in the WKB expansion. The other term represents the `remainder' of the WKB approximation and depends on the difference between an exact (numerical) expression and its WKB counterpart. This has to be dealt with by means of numerical approximation. The general results are specialized to the case of Schwarzschild-anti-de Sitter black hole geometries. The method is efficient enough to solve the semi-classical Einstein's equations taking into account the back-reaction from quantum fields on asymptotically anti-de Sitter black holes.

hep-th↗

arXiv2007

Branes and Black holes in Collision

We study the collision of a brane with a black hole. Our aim is to explore the topology changing process of perforation of a brane. The brane is described as a field theoretical domain wall in the context of an axion-like model consisting of a complex scalar effective field theory with approximate U(1) symmetry. We simulate numerically the dynamics of the collision and illustrate the transition from the configuration without a hole to the pierced one with the aid of a phase diagram. The process of perforation is found to depend on the collisional velocity, and, contrary to our expectation, we observe that above a critical value of the velocity, the black hole has no chance to perforate the wall. That is: high energy collisions do not assist piercing. We also show that, only when the model parameters are fine-tuned so that the energy scale of the string is very close to that of the domain wall, the collision of the wall with the black hole has a possibility to provide a mechanism to erase domain walls, if the hole expands. However, in such cases, domain walls will form with many holes edged by a string and therefore disappear eventually. Therefore this mechanism is unlikely to be a solution to the cosmological domain wall problem, although it may cause some minor effects on the evolution of a domain wall network.

hep-th↗

arXiv2006

Critical escape velocity of black holes from branes

In recent work we have shown that a black hole stacked on a brane escapes once it acquires a recoil velocity. This result was obtained in the {\it probe-brane} approximation, {\it i.e.}, when the tension of the brane is negligibly small. Therefore, it is not clear whether the effect of the brane tension may prevent the black hole from escaping for small recoil velocities. The question is whether a critical escape velocity exists. Here, we analyze this problem by studying the interaction between a Dirac-Nambu-Goto brane and a black hole assuming adiabatic (quasi-static) evolution. By describing the brane in a fixed black hole spacetime, which restricts our conclusions to lowest order effects in the tension, we find that the critical escape velocity does not exist for co-dimension one branes, while it does for higher co-dimension branes.

hep-th↗

arXiv2006

Dynamics of domain walls intersecting black holes

Previous studies concerning the interaction of branes and black holes suggested that a small black hole intersecting a brane may escape via a mechanism of reconnection. Here we consider this problem by studying the interaction of a small black hole and a domain wall composed of a scalar field and simulate the evolution of this system when the black hole acquires an initial recoil velocity. We test and confirm previous results, however, unlike the cases previously studied, in the more general set-up considered here, we are able to follow the evolution of the system also during the separation, and completely illustrate how the escape of the black hole takes place.

hep-th↗

arXiv2005

Escape of black holes from the brane

TeV-scale gravity theories allow the possibility of producing small black holes at energies that soon will be explored at the LHC or at the Auger observatory. One of the expected signatures is the detection of Hawking radiation, that might eventually terminate if the black hole, once perturbed, leaves the brane. Here, we study how the `black hole plus brane' system evolves once the black hole is given an initial velocity, that mimics, for instance, the recoil due to the emission of a graviton. The results of our dynamical analysis show that the brane bends around the black hole, suggesting that the black hole eventually escapes into the extra dimensions once two portions of the brane come in contact and reconnect. This gives a dynamical mechanism for the creation of baby branes.

hep-th↗

arXiv2004

Zeta Functions in Brane World Cosmology

We present a calculation of the zeta function and of the functional determinant for a Laplace-type differential operator, corresponding to a scalar field in a higher dimensional de Sitter brane background, which consists of a higher dimensional anti-de Sitter bulk spacetime bounded by a de Sitter section, representing a brane. Contrary to the existing examples, which all make use of conformal transformations, we evaluate the zeta function working directly with the higher dimensional wave operator. We also consider a generic mass term and coupling to curvature, generalizing previous results. The massless, conformally coupled case is obtained as a limit of the general result and compared with known calculations. In the limit of large anti-de Sitter radius, the zeta determinant for the ball is recovered in perfect agreement with known expressions, providing an interesting check of our result and an alternative way of obtaining the ball determinant.

hep-th↗

arXiv2003

Moduli stabilization in higher dimensional brane models

We consider a class of warped higher dimensional brane models with topology $M \times Σ\times S^1/Z_2$, where $Σ$ is a $D_2$ dimensional manifold. Two branes of codimension one are embedded in such a bulk space-time and sit at the orbifold fixed points. We concentrate on the case where an exponential warp factor (depending on the distance along the orbifold) accompanies the Minkowski $M$ and the internal space $Σ$ line elements. We evaluate the moduli effective potential induced by bulk scalar fields in these models, and we show that generically this can stabilize the size of the extra dimensions. As an application, we consider a scenario where supersymmetry is broken not far below the cutoff scale, and the hierarchy between the electroweak and the effective Planck scales is generated by a combination of redshift and large volume effects. The latter is efficient due to the shrinking of $Σ$ at the negative tension brane, where matter is placed. In this case, we find that the effective potential can stabilize the size of the extra dimensions (and the hierarchy) without fine tuning provided that the internal space $Σ$ is flat.

hep-th↗

arXiv2001

Quantized bulk fermions in the Randall-Sundrum brane model

The lowest order quantum corrections to the effective action arising from quantized massive fermion fields in the Randall-Sundrum background spacetime are computed. The boundary conditions and their relation with gauge invariance are examined in detail. The possibility of Wilson loop symmetry breaking in brane models is also analysed. The self-consistency requirements, previously considered in the case of a quantized bulk scalar field, are extended to include the contribution from massive fermions. It is shown that in this case it is possible to stabilize the radius of the extra dimensions but it is not possible to simultaneously solve the hierarchy problem, unless the brane tensions are dramatically fine tuned, supporting previous claims.

hep-th↗

arXiv2001

Fermion vacuum energies in brane world models

The fermion representations and boundary conditions in five dimensional anti de Sitter space are described in detail. In each case the one loop effective action is calculated for massless fermions. The possibility of topological or Wilson loop symmetry breaking is discussed.

hep-th↗