arXiv subjects

Margarita García Pérez

Publications and source records attributed to Margarita García Pérez.

At least 19 recordsLinked to original sources

arXiv2026

The large-$N$ Yang--Mills $Λ$-parameter from step scaling

We use the step-scaling method and results obtained at $N = 3, 5$ and $8$ to determine the $N$-dependence of the dynamically generated scale $Λ$ of $\mathrm{SU}(N)$ Yang--Mills theories. We implement the step-scaling method in a suitable finite-volume renormalization scheme based on twisted boundary conditions, introduced to effectively achieve large-$N$ volume independence, and on a coupling defined through the gradient flow. In the $\overline{\mathrm{MS}}$ scheme, we obtain the following values in terms of the gradient flow scale $t_0$: $\sqrt{8t_0}Λ_{\scriptscriptstyle{\overline{\mathrm{MS}}}} = 0.577(23)$, $0.632(32)$, and $0.611(43)$ for $N=3,5$ and $8$, respectively. They extrapolate to a large-$N$ value of: $\sqrt{8t_0}Λ_{\scriptscriptstyle{\overline{\mathrm{MS}}}} (N=\infty) = 0.639(36)$, and the $N$-dependence is given by $\sqrt{8t_0}Λ_{\scriptscriptstyle{\overline{\mathrm{MS}}}}(N)=0.639(36)[1-0.85(62)/N^2+\mathcal{O}(1/N^4)]$. This work represents the first calculation of the Yang--Mills $Λ$-parameter in the large-$N$ limit that does not rely on asymptotic scaling strategies.

hep-lat↗

arXiv2026

Universal Features of Chiral Symmetry Breaking in Large-$N$ QCD

We investigate the universal features of chiral symmetry breaking in large-$N$ QCD by comparing non-perturbative determinations of the low-lying Dirac spectrum with chiral Random Matrix Theory (RMT) predictions. Our numerical Monte Carlo calculations are based on a chiral lattice discretization of the Dirac operator, and exploit twisted volume reduction to reach $N$ as large as 841. Matching lattice data with RMT analytic results, we are able to extract the large-$N$ chiral condensate, which is compared with a recent determination obtained with non-chiral Wilson quarks from twisted volume-reduced models.

hep-lat↗

arXiv2026

Scale setting of SU($N$) Yang--Mills theory, topology and large-$N$ volume independence

We set the scale of SU($N$) Yang--Mills theories for $N=3,5,8$ and in the large-$N$ limit via gradient flow, as a first step towards the computation of the large-$N$ $Λ$-parameter using step scaling. We adopt twisted boundary conditions to achieve large-$N$ volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as $\sim 0.025$ fm for all the explored values of $N$, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-$N$ twisted volume reduction.

hep-lat↗

arXiv2026

Meson spectrum and low-energy constants in large-$N$ QCD

We present new non-perturbative results about the meson spectrum and the low-energy constants of QCD in the 't Hooft large-$N$ limit, $N\to\infty$ with $N_{\scriptscriptstyle{\rm f}}/N\to 0$. These are obtained from lattice Monte Carlo simulations of the Twisted Eguchi-Kawai (TEK) model up to $N=841$. More precisely, we will discuss: our findings for the meson mass spectrum; the determination of the radial Regge trajectories in the $π$ and $ρ$ channels; the computation of the coefficients of the $1/N$ expansion of the chiral condensate, of the pion decay constant, and of the next-to-leading-order coupling $\bar{\ell}_4$, up to $\mathcal{O}(1/N^3)$ from the combination of TEK and standard finite-$N$ results.

hep-lat↗

arXiv2025

Non-perturbative determination of meson masses and low-energy constants in large-$N$ QCD

We provide first-principles non-perturbative determinations of the low-lying meson mass spectrum of large-$N$ QCD in the 't Hooft limit $N_{\scriptscriptstyle{\rm f}}/N\to 0$, as well as of three low-energy constants appearing in the QCD chiral expansion: the quark condensate $Σ$, the pion decay constant $F_π$, and the next-to-leading-order coupling $\bar{\ell}_4$. Using the excited state masses in the $π$ and $ρ$ channels, we are able to investigate the behavior of their radial Regge trajectories. Concerning QCD low-energy constants, we are able to assess the magnitude of sub-leading corrections in $1/N$ by combining our $N=\infty$ results with previous finite-$N$ determinations. Our calculation exploits large-$N$ twisted volume reduction to efficiently perform numerical Monte Carlo simulations of the large-$N$ lattice discretized theory. We employ several values of $N$ up to $N=841$, 5 values of the lattice spacing, and several values of the quark mass, to achieve controlled continuum and chiral extrapolations.

hep-lat↗

arXiv2025

The mass of the gluino-glue bound state in large-$N$ $\mathcal{N}=1$ Supersymmetric Yang-Mills theory

We provide a first-principles non-perturbative determination of the mass of the lightest gluino-gluon bound state (gluino-glue) in large-$N$ $\mathcal{N}=1$ Supersymmetric Yang--Mills theory by means of numerical Monte Carlo simulations of the lattice-discretized theory, and exploiting large-$N$ twisted volume reduction. Our large-$N$ determination is consistent with naive extrapolation of previously-known $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ results.

hep-lat↗

arXiv2025

Scale setting of $\mathrm{SU}(N)$ Yang-Mills theories via Twisted Gradient Flow

We present preliminary results for the scale setting of $\mathrm{SU}(N)$ Yang-Mills theories using twisted boundary conditions and the gradient-flow scale $\sqrt{t_0}$. The end goal of this study is to determine the $\mathrm{SU(N)}$ $Λ$-parameter through the step-scaling method. The scale $\sqrt{t_0}$, being defined from the flowed action density of the gauge fields, is correlated with their topological charge and thus could be affected by topological freezing. We deal with this problem with the Parallel Tempering on Boundary Conditions algorithm, which we found to be effective for the same numerical setup in a previous work.

hep-lat↗

arXiv2024

The gluino condensate of large-$N$ SUSY Yang-Mills

We present the first lattice determination of the SUSY $\mathrm{SU}(N)$ Yang-Mills gluino condensate at large $N$. We exploit large-$N$ twisted volume reduction, and present two determinations based on the Banks-Casher relation and on a Gell-Mann-Oakes-Renner-like formula, both giving perfectly compatible results. By expressing the lattice results in the Novikov-Shifman-Vainshtein-Zakharov scheme, we are able for the first time to compare lattice and analytical computations, resolving a 40-year-long debate about the actual value and $N$-dependence of the gluino condensate.

hep-lat↗

arXiv2024

Nonperturbative determination of the ${\cal N} = 1$ supersymmetric Yang-Mills gluino condensate at large $N$

We present the first nonperturbative large-$N$ calculation of the $\mathcal{N}=1$ supersymmetric (SUSY) $\mathrm{SU}(N)$ Yang$-$Mills gluino condensate obtained by means of numerical simulations of the lattice-discretized theory, exploiting large-$N$ twisted volume reduction. We present two different determinations based, respectively, on the Banks$-$Casher formula and on the Gell-Mann$-$Oakes$-$Renner relation, both giving perfectly consistent results. By expressing the lattice results in the Novikov$-$Shifman$-$Vainshtein$-$Zakharov (NSVZ) scheme, we are able for the first time to compare numerical and analytic computations. Our most accurate determination of the Renormalization Group Invariant (RGI) gluino condensate gives $Σ_{\rm RGI} /Λ_{\rm NSVZ}^3 = [1.18\, (08)_{\rm stat}\, (12)_{\rm syst}]^3 = 1.64(33)_{\rm stat} \, (50)_{\rm syst} = 1.64(60)$, in agreement with the $N$-dependence and the value predicted by the weak coupling instanton-based approach $Σ_{\rm RGI} /Λ_{\rm NSVZ}^3 = 1$.

hep-th↗

arXiv2024

The $\mathrm{SU}(3)$ twisted gradient flow strong coupling without topological freezing

We investigate the role of topology on the lattice determination of the $\mathrm{SU}(3)$ strong coupling renormalized via gradient flow. To deal with the topological freezing of standard local algorithms, the definition of the coupling is usually projected onto the zero topological sector. However, it is not obvious that this definition is not biased by the loss of ergodicity. We instead avoid the topological freezing using a novel algorithm, the Parallel Tempering on Boundary Conditions. The comparison with a standard algorithm shows that, even in the case where the latter is severely frozen, one obtains the same projected coupling. Moreover, we show that the two definitions of the coupling, projected and non-projected, lead to the same flow of the renormalization scale. Our results imply that projecting the coupling does not affect the determination of the dynamically-generated scale of the theory $Λ$, as obtained through the step-scaling method.

hep-lat↗

arXiv2023

The Twisted Gradient Flow strong coupling with Parallel Tempering on Boundary Conditions

We present a proposal for calculating the running of the coupling constant of the $\mathrm{SU}(3)$ pure-gauge theory, which combines the Twisted Gradient Flow (TGF) renormalization scheme with Parallel Tempering on Boundary Conditions (PTBC). The TGF is a gradient flow-based renormalization scheme formulated in an asymmetric lattice with twisted boundary conditions. Combined with step scaling, it has been successfully used to calculate the $\mathrm{SU}(3)$ $Λ$ parameter. As with all gradient flow-based schemes, the coupling constant is highly correlated with the topological charge and affected by topology freezing, an issue addressed by projecting the determination of the coupling onto the zero topological sector. As an alternative to the zero-charge projection, we combine TGF with PTBC, by replicating multiple copies of the same lattice, interpolating between periodic and open boundary conditions in a parallel-tempered manner. We present a first exploration of these ideas by analyzing specific ensembles of $\mathrm{SU}(3)$ lattices with and without PTBC.

hep-lat↗

arXiv2022

SU(N) fractional instantons and the Fibonacci sequence

We study, by means of numerical methods, new $SU(N)$ self-dual instanton solutions on $\mathbf{R}\times \mathbf{T}^3$ with fractional topological charge $Q=1/N$. They are obtained on a box with twisted boundary conditions with a very particular choice of twist: both the number of colours and the 't Hooft $\mathbf{Z}_N$ fluxes piercing the box are taken within the Fibonacci sequence, i.e. $N=F_n$ (the $nth$ number in the series) and $|\vec m| = |\vec{k}|=F_{n-2}$. Various arguments based on previous works and in particular on ref. \cite{Chamizo:2016msz}, indicate that this choice of twist avoids the breakdown of volume independence in the large $N$ limit. These solutions become relevant on a Hamiltonian formulation of the gauge theory, where they represent vacuum-to-vacuum tunneling events lifting the degeneracy between electric flux sectors present in perturbation theory. We discuss the large $N$ scaling properties of the solutions and evaluate various gauge invariant quantities like the action density or Wilson and Polyakov loop operators.

hep-th↗

arXiv2021

Large $N$ simulation of the twisted reduced matrix model with an adjoint Majorana fermion

To investigate the properties of the large $N$ limit of $\mathcal{N} = 1$ SUSY Yang-Mills theory, we have started a study for a reduced matrix model with an adjoint Majorana fermion. The gauge action is based on the Wilson action and the adjoint-fermion one is the Wilson-Dirac action on a reduced lattice with twisted gauge boundary condition. We employ the RHMC algorithm in which the absolute value of the Pfaffian is incorporated. The sign of the Pfaffian is included with the re-weighting method and separately measured as an observable. In this talk, we show the configuration generation status towards the large $N$ limit and the behavior of the lowest/lower eigenvalue(s) of the Wilson-Dirac adjoint fermion operator. We investigated the sign of the Pfaffian and the critical hopping parameters for the chiral limit. The sign of the Pfaffian is always positive on the configurations we have generated. The critical hopping parameters derived from the eigenvalues of the Dirac operator are consistent with those derived from the PCAC mass relation with non-singlet flavor adjoint fermions.

hep-lat↗

arXiv2020

Meson spectrum in the large $N$ limit

We present the result of our computation of the lowest lying meson masses for SU(N) gauge theory in the large $N$ limit (with $N_f/N\longrightarrow 0$). The final values are given in units of the square root of the string tension, and with errors which account for both statistical and systematic errors. By using 4 different values of the lattice spacing we have seen that our results scale properly. We have studied various values of $N$ (169, 289 and 361) to monitor the N-dependence of the most sensitive quantities. Our methodology is based upon a first principles approach (lattice gauge theory) combined with large $N$ volume independence. We employed both Wilson fermions and twisted mass fermions with maximal twist. In addition to masses in the pseudoscalar, vector, scalar and axial vector channels, we also give results on the pseudoscalar decay constant and various remormalization factors.

hep-lat↗

arXiv2020

The meson spectrum of large N gauge theories

We present our preliminary results on the determination of the low lying meson spectrum for pure gauge theory in the large $N$ limit. Some results are also shown for the theory with two flavours of quarks in the adjoint representation.

hep-lat↗

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.

hep-lat↗

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.

hep-lat↗