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L. C. Q. Vilar

Publications and source records attributed to L. C. Q. Vilar.

At least 19 recordsLinked to original sources
arXiv2026

Pseudoscalar meson mass relations from a second-order phase transition

This work is divided in two parts. The first three sections review meson physics phenomenology, highlighting the history of pseudoscalar multiplet mass spectra research. We then propose a new approach for the mass mixing problem based exclusively on a second order phase transition principle. This development leads to new relations among the masses of the mesons in this nonet, which present a nice agreement with measurements. The quark constitutions and the mixing angle problem are also correctly addressed. After describing the spontaneous symmetry breaking process coming from this phenomenological analysis, we establish a field theory with the necessary elements that could reproduce theoretically such results. This is done in the second part of this work, where the one-loop quantum corrections are computed in full, with the cubic and quartic scalar vertices treated on the same footing. The resulting mass Lagrangian has a universal flavor structure, which forces a refined identification between the scalar components and the $η^{0}$--$η^{\prime\,0}$ states; we derive the general matching condition and present its minimal solution, which reproduces the phenomenological mixing matrix exactly. Combined with the gap equation of the scalar sector, the model is left with a single free coupling, which does not affect the mass predictions. We emphasize that this is a phenomenological model constructed to reproduce certain mass relations, not a first-principles derivation from QCD. Nevertheless, as we will show, the model's predictions for the pseudoscalar meson masses agree remarkably well with the observed QCD spectrum.

hep-ph↗
arXiv2024

Gribov Problem in the Eletroweak and Gluon Confined Theories

We show that gauge fields after a spontaneous symmetry breaking (SSB) mechanism do not have a Gribov problem along the broken directions. In order to make this proof, we describe a gauge fixing procedure inspired on Morse theory leading to the concept of a gauge fixing generating functional. This approach is specially suited in order to understand the unitary gauges of t Hooft. The conclusion is that after a SSB process, the generalized Faddeev-Popov operator acquires a positive definite value along the broken directions. We show how this works in the eletroweak $SU(2)XU(1)$ theory, where such a result is in fact expected as in this case the gauge fields acquire masses after the SSB. Then we apply this development to the $SL(3,c)$ confining model of [1]. The final result explains why such confining mechanism is actually a solution to Gribov problem for the confined gauge fields. These cases show that although confinement is not a general effect of the solution of the Gribov problem, as we can infer from the eletroweak example, its solution indeed seems to be necessary in order to achieve confinement. In the end, these conclusions allow us to speculate that the strong interaction confinement may be the result of some hidden SSB mechanism yet to be described.

hep-th↗
arXiv2023

A BRST Characterization of the Broken Phase Observables of the Confining Complex Theory

Some time ago we have introduced a route to provide confinement in the sense that particle excitations would appear from condensates of fields that do not have physical asymptotic states. We envisaged this mechanism in an asymmetric vacuum phase of a complex gauge field theory. More recently, we showed how to define a BRST operator to the broken phase of a generic spontaneous broken field theory. Our intention here is to apply these late concepts to the previous complex field theory in order to give a cohomological characterization of those condensed states as actual physical observables of this theory in its broken phase.

hep-th↗
arXiv2022

A BRST view of the spontaneous symmetry breaking

After the phase transition of a Grand Unified Theory (GUT), its single coupling splits into the couplings of the basic interactions. On the other side, the measurement of the Weinberg mixing angle in the eletroweak theory determines that the couplings associated to the SU(2) and U(1) symmetries were already distinct in its symmetric phase, before the electroweak breaking. This picture is consistent as we understand that such couplings evolve independently with the energy scale, meeting a common point together with the strong interaction coupling at the GUT scale. From a BRST symmetry point of view, this implies that each independent coupling should be associated to independent cocycles defined on a cohomological basis. The problem is that, before the GUT symmetry breaking, the BRST operator associated to this symmetric phase predicts a single Yang-Mills coupling. This sets the question of what should be the BRST operator of the asymmetric phase, that would allow for the splitting of this coupling but at the same time remain compatible with the BRST operator of the symmetric phase. In this work we proceed to answer this question.

hep-th↗
arXiv2020

Complex Chern-Simons and Gribov

We explore a contact point between two distinct approaches to the confinment problem. We show that BLG-ABJM like theories generate gauge propagators with just the complex pole structure prescribed by the Gribov scenario for confinemnt. This structure, known as i-particles in Gribov-Zwanziger theories, effectively allows the definition of composite operators with a positive Källén-Lehmann spectral representation for their two-point functions . Then, these operators satisfy the criteria to describe glue-ball condensates. We calculate the (first order) contribution to the two-point function of the gauge invariant condensate in an ABJM environment, showing its interpretation as a physical particle along Källén-Lehmann. In the meantime, we argue for the necessity of absorbing Witten's work on holomorphic complex theories in order to settle the physical interpretation of this non-perturbative scenario.

hep-th↗
arXiv2020

A path to confine gluons and fermions through complex gauge theory

We introduced here the study of a QCD based on a complex group. Our aim is to show that a gauge theory with a complex symmetry develops some of the features required for the description of a confined phase. This theory leads to gluons with propagations characteristic of i-particles, fundamental constituents of propagators in the Gribov scenario, together with a gluon propagating with the mode predicted by 't Hooft for the quark confinement. In this way, we present in this same theory a possible gluon condensate, together with a confining interquark potential after the coupling to fermions. This is a novelty, as, up to now, all theories of the GZ kind do not generate quark confinement.

hep-th↗
arXiv2018

Confining Potentials

We use the t'Hoft-Wilson method for the generation of static fermions potential in order to derive a class of confining potentials which can describe the quark confinement. A general pattern for the construction of propagators through the localization of non-local actions is uncovered.

hep-th↗
arXiv2014

Revisiting Gribov's Copies Inside The Horizon

In this work, we recover the problem of legitimate topologically trivial Gribov copies inside the Gribov horizon. We avoid the reducibility problem which hampered the standard construction of van Baal, and then we are able to build a valid example with spherical symmetry. We also apply the same technique in the presence of a background of a Polyakov instanton in a Euclidian 3D spacetime, in order to study the effect of a non trivial environment in the generation of multiple copies inside the horizon.

hep-th↗
arXiv2012

On the zero modes of the Faddev-Popov operator in the Landau gauge

Following Henyey procedure, we construct examples of zero modes of the Faddev-Popov operator in the Landau gauge in Euclidean space in D dimensions, for both SU(2) and SU(3 groups. We consider gauge field configurations $A^a_μ$ which give rise to a field strength, $F^a_{μν} =\partial_μA^a_ν-\partial_νA^a_μ+ f^{abc}A^b_μA^c_ν$, whose nonlinear term, $ f^{abc}A^b_μA^c_ν$, turns out to be nonvanishing. To our knowledge, this is the first time where such a non-abelian configuration is explicitly obtained in the case of SU(3) in 4D.

hep-th↗
arXiv2011

Gribov as a Phase Transition

Our goal will be the description of a theory of Gribov's type as a physical process of phase transition in the context of a spontaneous symmetry breaking. We mainly focus at the quantum stability of the whole process.

hep-th↗
arXiv2010

On the Renormalizability of Noncommutative U(1) Gauge Theory - an Algebraic Approach

We investigate the quantum effects of the nonlocal gauge invariant operator $\frac{1}{{}{D}^{2}}{F}_{μν}\ast \frac{1}{{}{D}^{2}}{F}^{μν}$ in the noncommutative U(1) action and its consequences to the infrared sector of the theory. Nonlocal operators of such kind were proposed to solve the infrared problem of the noncommutative gauge theories evading the questions on the explicit breaking of the Lorentz invariance. More recently, a first step in the localization of this operator was accomplished by means of the introduction of an extra tensorial matter field, and the first loop analysis was carried out $(Eur.Phys.J.\textbf{C62}:433-443,2009)$. We will complete this localization avoiding the introduction of new degrees of freedom beyond those of the original action by using only BRST doublets. This will allow us to make a complete BRST algebraic study of the renormalizability of the theory, following Zwanziger's method of localization of nonlocal operators in QFT.

hep-th↗
arXiv2008

Seiberg-Witten map for the 4D noncommutative BF theory

We describe the Seiberg-Witten map for the 4D noncommutative BF theory (NCBF). We establish the existence of a map taking the abelian NCBF into its commutative version, in agreement with the hypothesis that such maps are available for any noncommutative theory with Schwarz type topological sectors.

hep-th↗
arXiv2006

On The Complete Seiberg-Witten Map For Theories With Topological Terms

The SW map problem is formulated and solved in the BRST cohomological approach. The well known ambiguities of the SW map are shown to be associated to distinct cohomological classes. This analysis is applied to the noncommutative Chern-Simons action resulting in the emergence of $θ$-dependent terms in the commutative action which come from the nontrivial ambiguities. It is also shown how a specific cohomological class can be choosen in order to map the noncommutative Maxwell-Chern-Simons theory into the commutative one.

hep-th↗
arXiv2001

An Algebraic Criterion for the Ultraviolet Finiteness of Quantum Field Theories

An algebraic criterion for the vanishing of the beta function for renormalizable quantum field theories is presented. Use is made of the descent equations following from the Wess-Zumino consistency condition. In some cases, these equations relate the fully quantized action to a local gauge invariant polynomial. The vanishing of the anomalous dimension of this polynomial enables us to establish a nonrenormalization theorem for the beta function $β_g$, stating that if the one-loop order contribution vanishes, then $β_g$ will vanish to all orders of perturbation theory. As a by-product, the special case in which $β_g$ is only of one-loop order, without further corrections, is also covered. The examples of the N=2,4 supersymmetric Yang-Mills theories are worked out in detail.

hep-th↗
arXiv2000

Vector Supersymmetry of 2D Yang-Mills Theory

The vector supersymmetry of the 2D topological BF model is extended to 2D Yang-Mills. The consequences of the corresponding Ward identity on the ultraviolet behavior of the theory are analyzed.

hep-th↗
arXiv2000

BRST Cohomology of N=2 Super-Yang-Mills Theory in 4D

The BRST cohomology of the N=2 supersymmetric Yang-Mills theory in four dimensions is discussed by making use of the twisted version of the N=2 algebra. By the introduction of a set of suitable constant ghosts associated to the generators of N=2, the quantization of the model can be done by taking into account both gauge invariance and supersymmetry. In particular, we show how the twisted N=2 algebra can be used to obtain in a straightforward way the relevant cohomology classes. Moreover, we shall be able to establish a very useful relationship between the local gauge invariant polynomial $trϕ^2$ and the complete N=2 Yang-Mills action. This important relation can be considered as the first step towards a fully algebraic proof of the one-loop exactness of the N=2 beta function.

hep-th↗
arXiv2000

Perturbative Beta Function of N=2 Super Yang-Mills Theories

An algebraic proof of the nonrenormalization theorem for the perturbative beta function of the coupling constant of N=2 Super Yang-Mills theory is provided. The proof relies on a fundamental relationship between the N=2 Yang-Mills action and the local gauge invariant polynomial Tr phi^2, phi(x) being the scalar field of the N=2 vector gauge multiplet. The nonrenormalization theorem for the beta function follows from the vanishing of the anomalous dimension of Tr phi^2.

hep-th↗