arXiv subjects

Pablo Pais

Publications and source records attributed to Pablo Pais.

33 records · Page 2Linked to original sources

arXiv2019

(Anti-)de Sitter, Poincaré, Super symmetries, and the two Dirac points of graphene

We propose two different high-energy-theory correspondences with graphene (and related materials) scenarios, associated to grain boundaries, that are topological defects for which both Dirac points are necessary. The first correspondence points to a $(3+1)$-dimensional theory, with nonzero torsion, with spatiotemporal gauge group $SO(3,1)$, locally isomorphic to the Lorentz group in $(3+1)$ dimensions, or to the de Sitter group in $(2+1)$ dimensions. The other correspondence treats the two Dirac fields as an internal symmetry doublet, and it is linked here with unconventional supersymmetry with $SU(2)$ internal symmetry. Our results are suggestive, rather than conclusive, and pave the way to the inclusion of grain boundaries in the emergent field theory picture associated with these materials, whereas disclinations and dislocations have been already well explored.

hep-th↗

arXiv2019

Gribov horizon, Polyakov loop and finite temperature

We consider finite-temperature $SU(2)$ gauge theory in the continuum formulation. Choosing the Landau gauge, the existing gauge copies are taken into account by means of the Gribov-Zwanziger quantization scheme, which entails the introduction of a dynamical mass scale (Gribov mass) directly influencing the Green functions of the theory. Here, we determine simultaneously the Polyakov loop (vacuum expectation value) and Gribov mass in terms of temperature, by minimizing the vacuum energy with respect to the Polyakov-loop parameter and solving the Gribov gap equation. The main result is that the Gribov mass directly feels the deconfinement transition, visible from a cusp occurring at the same temperature where the Polyakov loop becomes nonzero. Finally, problems for the pressure at low temperatures are reported.

hep-th↗

arXiv2019

Generalized uncertainty principle in graphene

We show that, by going beyond the low-energy approximation for which the dispersion relations of graphene are linear, the corresponding emergent field theory is a specific generalization a Dirac field theory. The generalized Dirac Hamiltonians one obtains are those compatible with specific generalizations of the uncertainty principle. We also briefly comment on the compatibility of the latter with noncommuting positions, $[x_i,x_j] \neq 0$, and on their possible physical realization.

hep-th↗

arXiv2019

Chiral Anomaly Calculation in the Extended Coupled Rarita-Schwinger Mode

We recalculate the chiral anomaly in the Abelian gauge model in which a spin-$\frac{1}{2}$ field is directly coupled to a Rarita-Schwinger spin-$\frac{3}{2}$ field, using the extended theory in which there is an exact fermionic gauge invariance. Since the standard gauge fixing and ghost analysis applies to this theory, the ghost contribution to the chiral anomaly is $-1$ times the standard chiral anomaly for spin-$\frac{1}{2}$. Calculation of the fermion loop Feynman diagrams contributing to the coupled model anomaly gives a result of $6$ times the standard anomaly, so the total anomaly is $5$ times the standard anomaly. This agrees with the result obtained from the unextended model taking the ghost contribution there as $0$, corresponding to a non-propagating ghost arising from exponentiating the second class constraint determinant, together with the fermion loop anomaly contribution in the unextended model of $5$ times the standard anomaly.

hep-th↗

arXiv2017

Canonical Field Anticommutators in the Extended Gauged Rarita-Schwinger Theory

We reexamine canonical quantization of the gauged Rarita-Schwinger theory using the extended theory, incorporating a dimension $\frac{1}{2}$ auxiliary spin-$\frac{1}{2}$ field $Λ$, in which there is an exact off-shell gauge invariance. In $Λ=0$ gauge, which reduces to the original unextended theory, our results agree with those found by Johnson and Sudarshan, and later verified by Velo and Zwanziger, which give a canonical Rarita-Schwinger field Dirac bracket that is singular for small gauge fields. In gauge covariant radiation gauge, the Dirac bracket of the Rarita-Schwinger fields is nonsingular, but does not correspond to a positive semi-definite anticommutator, and the Dirac bracket of the auxiliary fields has a singularity of the same form as found in the unextended theory. These results indicate that gauged Rarita-Schwinger theory is somewhat pathological, and cannot be canonically quantized within a conventional positive semi-definite metric Hilbert space. We leave open the questions of whether consistent quantizations can be achieved by using an indefinite metric Hilbert space, by path integral methods, or by appropriate couplings to conventional dimension $\frac{3}{2}$ spin-$\frac{1}{2}$ fields.

hep-th↗

arXiv2017

The Gribov problem in presence of background field for $SU(2)$ Yang-Mills theory

The Gribov problem in the presence of a background field is analyzed: in particular, we study the Gribov copies equation in the Landau-De Witt gauge as well as the semi-classical Gribov gap equation. As background field, we choose the simplest non-trivial one which corresponds to a constant gauge potential with non-vanishing component along the Euclidean time direction. This kind of constant non-Abelian background fields is very relevant in relation with (the computation of) the Polyakov loop but it also appears when one considers the non-Abelian Schwinger effect. We show that the Gribov copies equation is affected directly by the presence of the background field, constructing an explicit example. The analysis of the Gribov gap equation shows that the larger the background field, the smaller the Gribov mass parameter. These results strongly suggest that the relevance of the Gribov copies (from the path integral point of view) decreases as the size of the background field increases.

hep-th↗

arXiv2016

Dynamical Contents of Unconventional Supersymmetry

The Dirac Hamiltonian formalism is applied to a system in $(2+1)$-dimensions consisting of a Dirac field $ψ$ minimally coupled to Chern-Simons $U(1)$ and $SO(2,1)$ connections, $A$ and $ω$, respectively. This theory is connected to a supersymmetric Chern-Simons form in which the gravitino has been projected out (unconventional supersymmetry) and, in the case of a flat background, corresponds to the low energy limit of graphene. The separation between first-class and second-class constraints is performed explicitly, and both the field equations and gauge symmetries of the Lagrangian formalism are fully recovered. The degrees of freedom of the theory in generic sectors shows that the propagating states correspond to fermionic modes in the background determined by the geometry of the graphene sheet and the nondynamical electromagnetic field. This is shown for the following canonical sectors: i) a conformally invariant generic description where the spinor field and the dreibein are locally rescaled; ii) a specific configuration for the Dirac fermion consistent with its spin, where Weyl symmetry is exchanged by time reparametrizations; iii) the vacuum sector $ψ=0$, which is of interest for perturbation theory. For the latter the analysis is adapted to the case of manifolds with boundary, and the corresponding Dirac brackets together with the centrally extended charge algebra are found. Finally, the $SU(2)$ generalization of the gauge group is briefly treated, yielding analogous conclusions for the degrees of freedom.

hep-th↗

arXiv2016

Comments on the compatibility of thermodynamic equilibrium conditions with lattice propagators

In this paper the compatibility is analyzed of the non-perturbative equations of state of quarks and gluons arising from the lattice with some natural requirements for self-gravitating objects at equilibrium: the existence of an equation of state (namely, the possibility to define the pressure as a function of the energy density), the absence of superluminal propagation and Le Chatelier's principle. It is discussed under which conditions it is possible to extract an equation of state (in the above sense) from the non-perturbative propagators arising from the fits of the latest lattice data. In the quark case, there is a small but non-vanishing range of temperatures in which it is not possible to define a single-valued functional relation between density and pressure. Interestingly enough, a small change of the parameters appearing in the fit of the lattice quark propagator (of around 10~\%) could guarantee the fulfillment of all the three conditions (keeping alive, at the same time, the violation of positivity of the spectral representation, which is the expected signal of confinement). As far as gluons are concerned, the analysis shows very similar results. Whether or not the non-perturbative quark and gluon propagators satisfy these conditions can have a strong impact on the estimate of the maximal mass of quark stars.

hep-th↗

arXiv2015

Revisiting the gauge fields of strained graphene

We show that, when graphene is only subject to strain, the spin connection gauge field that arises plays no measurable role, but when intrinsic curvature is present and strain is small, spin connection dictates most the physics. We do so by showing that the Weyl field associated with strain is a pure gauge field and no constraint on the $(2+1)$-dimensional spacetime appears. On the other hand, for constant intrinsic curvature that also gives a pure-gauge Weyl field, we find a classical manifestation of a quantum Weyl anomaly, descending from a constrained spacetime. We are in the position to do this because we find the equations that the conformal factor in $(2+1)$-dimensions has to satisfy, that is a nontrivial generalization to $(2+1)$-dimensions of the classic Liouville equation of differential geometry of surfaces. Finally, we comment on the peculiarities of the only gauge field that can describe strain, that is the well known {\it pseudogauge field} $A_1 \sim u_{11} - u_{22}$ and $A_2 \sim u_{12}$, and conclude by offering some scenarios of fundamental physics that this peculiar field could help to realize.

hep-th↗

arXiv2015

Supersymmetric 3D model for gravity with $SU(2)$ gauge symmetry, mass generation and effective cosmological constant

A Chern--Simons system in $2+1$ dimensions invariant under local Lorentz rotations, $SU(2)$ gauge transformations, and local $\mathcal{N}=2$ supersymmetry transformations is proposed. The field content is that of $(2+1)$-gravity plus an $SU(2)$ gauge field, a spin-1/2 fermion charged with respect to $SU(2)$ and a trivial free abelian gauge field. A peculiarity of the model is the absence of gravitini, although it includes gravity and supersymmetry. Likewise, no gauginos are present. All the parameters involved in the system are either protected by gauge invariance or emerge as integration constants. An effective mass and effective cosmological constant emerge by spontaneus breaking of local scaling invariance. The vacuum sector is defined by configurations with locally flat Lorentz and $SU(2)$ connections sporting nontrivial global charges. Three-dimensional Lorentz-flat geometries are spacetimes of locally constant negative --or zero--, Riemann curvature, which include Minkowski space, AdS$_3$, BTZ black holes, and point particles. These solutions admit different numbers of globally defined, covariantly constant spinors and are therefore good candidates for stable ground states. The fermionic sector in this system could describe the dynamics of electrons in graphene in the long wavelength limit near the Dirac points, with the spin degree of freedom of the electrons represented by the $SU(2)$ label. If this is the case, the $SU(2)$ gauge field would produce a spin-spin interaction giving rise to strong correlation of electron pairs.

hep-th↗

arXiv2014

Local supersymmetry without SUSY partners

A gauge theory for a superalgebra that includes an internal gauge (G) and local Lorentz algebras, and that could describe the low energy particle phenomenology is constructed. These two symmetries are connected by fermionic supercharges. The system includes an internal gauge connection 1-form $A$, a spin-1/2 Dirac spinor $ψ$, the Lorentz connection $ω$, and the vielbein $e$. The connection one-form is in the adjoint representation of G, while $ψ$ is in the fundamental. In contrast to standard supergravity, the metric is not a fundamental field and is in the center of the superalgebra: it is not only invariant under the internal gauge group and under Lorentz transformations, but is also invariant under supersymmetry. The features of this theory that mark the difference with standard supersymmetry are: A) The number of fermionic and bosonic states is not necessarily the same; B) There are no superpartners with equal mass, "bosoninos", sleptons and squarks are absent; C) Although this supersymmetry originates in a local gauge theory and gravity is included, there is no gravitino; D) Fermions acquire mass from their coupling to the background or from self-couplings, while bosons remain massless. In odd dimensions, the Chern-Simons form provides an action that is quasi-invariant under the entire superalgebra. In even dimensions, the Yang-Mills form $ < F *F>$ is the only natural option, and the symmetry breaks down to [G x SO(1,D-1)]. In 4D, the construction follows the Townsend - Mac Dowell-Mansouri approach. Due to the absence of osp(4|2)-invariant traces in four dimensions, the resulting Lagrangian is only invariant under [U(1) x SO(3,1)], and includes a Nambu--Jona-Lasinio term. In this case, the Lagrangian depends on a single dimensionful parameter that fixes Newton's constant, the cosmological constant and the NJL coupling.

hep-th↗

arXiv2014

Gribov gap equation at finite temperature

In this paper the Gribov gap equation at finite temperature is analyzed. The solutions of the gap equation (which depend explicitly on the temperature) determine the structure of the gluon propagator within the semi-classical Gribov approach. The present analysis is consistent with the standard confinement scenario for low temperatures, while for high enough temperatures, deconfinement takes place and a free gluon propagator is obtained. It also suggests the presence of the so-called semi-quark-gluon-plasma phase in between the confined and quark-gluon plasma phases.

hep-th↗

arXiv2014

The BTZ black hole as a Lorentz-flat geometry

It is shown that 2+1 dimensional anti-de Sitter spacetimes are Lorentz-flat. This means, in particular, that any simply-connected patch of the BTZ black hole solution can be endowed with a Lorentz connection that is locally pure gauge. The result can be naturally extended to a wider class of black hole geometries and point particles in three-dimensional spacetime.

gr-qc↗

arXiv2012

Survey of Kozai Dynamics Beyond Neptune

We study the Kozai dynamics affecting the orbital evolution of transneptunian objects being captured or not in MMR with Neptune. We provide energy level maps of the type (ω,q) describing the possible orbital paths from Neptune up to semimajor axis of hundreds of AU. The dynamics for non resonant TNOs with perihelion distances, q, outside Neptune's orbit, a_N, is quite different from the dynamics of TNOs with q < a_N, already studied in previous works. While for the last case there are stable equilibrium points at ω = 0\circ, 90\circ, 180\circ and 270\circ in a wide range of orbital inclinations, for the former case it appears a family of stable equilibrium points only at a specific value of the orbital inclination, i \sim 62\circ, that we call critical inclination. We show this family of equilibrium points is generated by a mechanism analogue to which drives the dynamics of an artificial satellite perturbed by an oblate planet. The planetary system also generates an oscillation in the longitude of the perihelion of the TNOs with i \sim 46\circ, being Eris a paradigmatic case. We discuss how the resonant condition with Neptune modify the energy level curves and the location of equilibrium points. The asymmetric librations of resonances of the type 1:N generate a distortion in the energy level curves and in the resulting location of the equilibrium points in the phase space (ω,q). We study the effect on the Kozai dynamics due to the diffusion process in "a" that occurs in the Scattered Disk. We show that a minimum orbital inclination is required to allow substantial variations in perihelion distances once the object is captured in MMR and that minimum inclination is greater for greater semimajor axis.

astro-ph.EP↗

arXiv2011

Gauged WZW models for space-time groups and gravitational actions

In this paper we investigate gauged Wess-Zumino-Witten models for space-time groups as gravitational theories, following the trend of recent work by Anabalon, Willison and Zanelli. We discuss the field equations in any dimension and study in detail the simplest case of two space-time dimensions and gauge group SO(2,1). For this model we study black hole solutions and we calculate their mass and entropy which resulted in a null value for both.

hep-th↗