arXiv subjects

Antonio González-Arroyo

Publications and source records attributed to Antonio González-Arroyo.

At least 37 records · Page 2Linked to original sources

arXiv2019

Numerical stochastic perturbation theory applied to the twisted Eguchi-Kawai model

We present the results of an exploratory study of the numerical stochastic perturbation theory (NSPT) applied to the four dimensional twisted Eguchi-Kawai (TEK) model. We employ a Kramers type algorithm based on the Generalized Hybrid Molecular Dynamics (GHMD) algorithm. We have computed the perturbative expansion of square Wilson loops up to $O(g^8)$. The results of the first two coefficients (up to $O(g^4)$) have a high precision and match well with the exact values. The next two coefficients can be determined and even extrapolated to large $N$, where they should coincide with the corresponding coefficients for ordinary Yang-Mills theory on an infinite lattice. Our analysis shows the behaviour of the probability distribution for each coefficient tending to Gaussian for larger $N$. The results allow us to establish the requirements to extend this analysis to much higher order.

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arXiv2018

The spectrum of 2+1 dimensional Yang-Mills theory on a twisted spatial torus

We compute and analyse the low-lying spectrum of 2+1 dimensional $SU(N)$ Yang-Mills theory on a spatial torus of size $l\times l$ with twisted boundary conditions. This paper extends our previous work \cite{Perez:2013dra}. In that paper we studied the sector with non-vanishing electric flux and concluded that the energies only depend on the parameters through two combinations: $x=λN l /(4π)$ (with $λ$ the 't Hooft coupling) and the twist angle $\tilde θ$ defined in terms of the magnetic flux piercing the two-dimensional box. Here we made a more complete study and we are able to condense our results, obtained by non-perturbative lattice methods, into a simple expression which has important implications for the absence of tachyonic instabilities, volume independence and non-commutative field theory. Then we extend our study to the sector of vanishing electric flux. We conclude that the onset of the would-be large-volume glueball states occurs at an approximately fixed value of $x$, much before the stringy torelon states have become very massive.

hep-th↗

arXiv2017

Perturbative contributions to Wilson loops in twisted lattice boxes and reduced models

We compute the perturbative expression of Wilson loops up to order $g^4$ for SU($N$) lattice gauge theories with Wilson action on a finite box with twisted boundary conditions. Our formulas are valid for any dimension and any irreducible twist. They contain as a special case that of the 4-dimensional Twisted Eguchi-Kawai model for a symmetric twist with flux $k$. Our results allow us to analyze the finite volume corrections as a function of the flux. In particular, one can quantify the approach to volume independence at large $N$ as a function of flux $k$. The contribution of fermion fields in the adjoint representation is also analyzed.

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arXiv2016

`t Hooft model on the Lattice

Lattice results are presented for the meson spectrum of 1+1 dimensional gauge theory at large $N$, using the Twisted Eguchi-Kawai model. Comparison is made to the results obtained by `t Hooft in the light cone gauge.

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arXiv2016

Meson masses and decay constants at large $N$

Meson masses and decay constants in the large $N$ limit of SU($N$) gauge theory are determined using the twisted Eguchi-Kawai reduced model. To this end, we make use of a recently defined smearing method valid on the one-point lattice. This procedure, in combination with a variational analysis, allows to obtain reliable values for these quantities.

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arXiv2015

Large N meson propagators from twisted space-time reduced model

Recently, we proposed a new method to calculate meson propagators in the large $N$ limit from twisted space-time reduced model. In this note, we give simulation details for obtaining meson spectra and discuss the smearing technique which should improve the signal of meson propagators in future works.

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arXiv2015

Large N meson masses from a matrix model

We explain how to compute meson masses in the large $N$ limit using the twisted Eguchi-Kawai model. A very simple formula is derived, and we show how it leads in a fast and efficient way to results which are in fairly good agreement with other determinations. The method is easily extensible to reduced models with dynamical fermions based on the twisted reduction idea.

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arXiv2015

Mass anomalous dimension of Adjoint QCD at large N from twisted volume reduction

In this work we consider the $SU(N)$ gauge theory with two Dirac fermions in the adjoint representation, in the limit of large $N$. In this limit the infinite-volume physics of this model can be studied by means of the corresponding twisted reduced model defined on a single site lattice. Making use of this strategy we study the reduced model for various values of $N$ up to 289. By analyzing the eigenvalue distribution of the adjoint Dirac operator we test the conformality of the theory and extract the corresponding mass anomalous dimension.

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arXiv2015

A comparison of updating algorithms for large N reduced models

We investigate Monte Carlo updating algorithms for simulating $SU(N)$ Yang-Mills fields on a single-site lattice, such as for the Twisted Eguchi-Kawai model (TEK). We show that performing only over-relaxation (OR) updates of the gauge links is a valid simulation algorithm for the Fabricius and Haan formulation of this model, and that this decorrelates observables faster than using heat-bath updates. We consider two different methods of implementing the OR update: either updating the whole $SU(N)$ matrix at once, or iterating through $SU(2)$ subgroups of the $SU(N)$ matrix, we find the same critical exponent in both cases, and only a slight difference between the two.

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arXiv2014

The $SU(\infty)$ twisted gradient flow running coupling

We measure the running of the $SU(\infty)$ 't Hooft coupling by performing a step scaling analysis of the Twisted Eguchi-Kawai (TEK) model, the SU($N$) gauge theory on a single site lattice with twisted boundary conditions. The computation relies on the conjecture that finite volume effects for SU(N) gauge theories defined on a 4-dimensional twisted torus are controlled by an effective size parameter $\tilde l = l \sqrt{N}$, with $l$ the torus period. We set the scale for the running coupling in terms of $\tilde l$ and use the gradient flow to define a renormalized 't Hooft coupling $λ(\tilde l)$. In the TEK model, this idea allows the determination of the running of the coupling through a step scaling procedure that uses the rank of the group as a size parameter. The continuum renormalized coupling constant is extracted in the zero lattice spacing limit, which in the TEK model corresponds to the large $N$ limit taken at fixed value of $λ(\tilde l)$. The coupling constant is thus expected to coincide with that of the ordinary pure gauge theory at $N =\infty$. The idea is shown to work and permits us to follow the evolution of the coupling over a wide range of scales. At weak coupling we find a remarkable agreement with the perturbative two-loop formula for the running coupling.

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arXiv2014

Glueball masses in 2+1 dimensional SU(N) gauge theories with twisted boundary conditions

We analyze 2+1 dimensional Yang-Mills theory regularized on a lattice with twisted boundary conditions in the spatial directions. In previous work it was shown that the observables in the non-zero electric flux sectors obey the so-called $x$-scaling, i.e. depend only on the dimensionless variable $x\propto NL/b$ and the angle $\tildeθ$ given by the parameters of the twist ($L$ being the length of the spatial torus and $b$ the inverse 't Hooft coupling). It is conjectured that this scaling is obeyed by all physical quantities. In this work we extend the previous analyses to the zero electric flux (glueball) sector. We study the mass of the lightest scalar glueball in two theories with different $N$ but matching $x$ and $\tildeθ$ in a wide range of couplings from the perturbative small-volume regime to the non-perturbative one. We find that the results are consistent with the $x$-scaling hypothesis.

hep-lat↗

arXiv2014

TEK twisted gradient flow running coupling

We measure the running of the twisted gradient flow coupling in the Twisted Eguchi-Kawai (TEK) model, the SU(N) gauge theory on a single site lattice with twisted boundary conditions in the large N limit.

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arXiv2014

String tension from smearing and Wilson flow methods

Recently, we proposed a new method to extract the string tension from 4-dimensionally smeared Wilson loops. In this talk, we first show that the results obtained using this smearing method are identical to those obtained by Wilson flow, once the time step is sufficiently small. We then demonstrate the practical advantage of our method by applying it to the calculation of string tension in SU(3) Yang-Mills theory.

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arXiv2014

Quantum corrections to vortex masses and energies

We study the 2+1 dimensional abelian Higgs model defined on a spatial torus at critical self-coupling. We propose a method to compute the quantum contribution to the mass of the ANO vortex and to multi-vortex energies. The one-loop quantum correction to multi-vortex energies is computed analytically at the critical value of the torus area (Bradlow limit). For other values of the area one can set up an expansion around this critical area (Bradlow parameter expansion). The method is explained and the next-to-leading term explicitly evaluated. To this order, the resulting energies depend on the torus periods, but not on the vortex positions.

hep-th↗

arXiv2013

Twisted reduction in large N QCD with adjoint Wilson fermions

The twisted space-time reduced model of large $N$ QCD with various flavours of adjoint Wilson fermions is constructed applying the symmetric twist boundary conditions with flux $k$. The models with one and two flavours show distinctive behaviours. For the two flavor case, the string tension, calculated at $N=289$, approaches zero as we decrease the quark mass in a way consistent with the theory being governed by an infrared fixed point. In contrast, the string tension for the case of a single adjoint Wilson fermion remains finite as the quark mass decreases to zero, supporting that this is a confining theory.

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arXiv2013

Spatial volume dependence for 2+1 dimensional SU(N) Yang-Mills theory

We study the 2+1 dimensional SU(N) Yang-Mills theory on a finite two-torus with twisted boundary conditions. Our goal is to study the interplay between the rank of the group N, the length of the torus L and the Z_N magnetic flux. After presenting the classical and quantum formalism, we analyze the spectrum of the theory using perturbation theory to one-loop and using Monte Carlo techniques on the lattice. In perturbation theory, results to all orders depend on the combination x=λNL and an angle defined in terms of the magnetic flux (λ is 't Hooft coupling). Thus, fixing the angle, the system exhibits a form of volume independence (NL dependence). The numerical results interpolate between our perturbative calculations and the confinement regime. They are consistent with x-scaling and provide interesting information about the k-string spectrum and effective string theories. The occurrence of tachyonic instabilities is also analysed. They seem to be avoidable in the large N limit with a suitable scaling of the magnetic flux.

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arXiv2013

Twisted space-time reduced model of large N QCD with two adjoint Wilson fermions

The space-time reduced model of large N QCD with two adjoint Wilson fermions is constructed by applying the symmetric twist boundary conditions with non-vanishing flux $k$. For large but finite $N=L^2$, the model should behave as the large N version of the ordinary lattice gauge model on a $V=L^4$ space-time volume. We perform a comparison of the $N$ dependence of several quantities in this model and in the $k$=0 model (corresponding to periodic boundary conditions). Although the Z$^4$(N) symmetry seems unbroken in all cases, the N-dependence analysis favours the use of the same values of $k$ and $L$ for which the symmetry is also unbroken in the pure gauge case. In particular, the $k=0$ model, studied recently by several authors, shows a large and irregular dependence on $N$ within our region of parameters. This makes this reduced model very impractical for extracting physical information about the large N lattice theory. On the contrary, the model for $N=289=17^2$ and large enough $k$ gives consistent results, even for extended observables as Wilson loops $W(R,T)$ up to $R,T$=8, matching the expected behaviour for the lattice model with a $17^4$ space-time volume.

hep-lat↗

arXiv2013

Twisted reduction in large $N$ QCD with adjoint Wilson fermions

The twisted reduced model of large $N$ QCD with two adjoint Wilson fermions is studied numerically using the Hybrid Monte Carlo method. This is the one-site model, whose large $N$ limit (large volume limit) is expected to be conformal or nearly conformal. The string tension calculated at $N$=289 approaches zero as we decrease quark mass and the preliminary value of the mass anomalous dimension $γ_*$ is close to one if we assume that the theory is governed by an infrared fixed point. We also discuss the twisted reduced model with single adjoint Wilson fermion. The string tension remains finite as the quark mass decreases to zero, supporting that this is the confining theory.

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