arXiv subjects

Antonio González-Arroyo

Publications and source records attributed to Antonio González-Arroyo.

At least 19 recordsLinked to original sources

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

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

A $T_2 \times R^2$ roadmap to Confinement in SU(2) Yang-Mills theory

We study the behaviour of \SU{2} Yang-Mills fields on a $T_2\times R^2$ geometry where the two-torus is equipped with twisted boundary conditions. We monitor the evolution of the dynamics of the system as a function of the torus size $l_s$. For small sizes the behaviour of the system is well understood in terms of semiclassical predictions. In our case, the long distance structure is that of a two-dimensional gas of vortex-like fractional instantons with size and density growing with $l_s$. Our lattice Monte Carlo simulations confirm the semiclassical predictions and allow the determination of the relevant scale signalling the transition to the non-dilute situation. At low densities the string tension takes the standard value of a 2D center-vortex gas, growing with the density and approaching the value measured at infinite volume. Our work includes preliminary studies of the extension to \SU{N} and to the region of large sizes in which boundary conditions are irrelevant, and all physical scales are determined by the $Λ$ parameter.

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

Fractional instantons and Confinement: first results on a $T_2\times R^2$ roadmap

We report results obtained for SU(2) Yang-Mills theory on a four dimensional torus with two directions much smaller than the other two. The small 2-torus is equipped with twisted boundary conditions. This construction provides a way to interpolate from a region in which semiclassical methods can be applied (for small 2-torus size) to the standard infinite volume case. Our simulations at small torus sizes show how the topological charge and the string tension result from a gas of vortex-like fractional instantons. As the size becomes larger the density increases and the separation of structures tends to a constant in agreement with the fractional instanton liquid model picture of the Yang-Mills vacuum.

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

Identifying topological structures with adjoint filtering method

We present new investigations on the Adjoint Filtering Method (AFM), a proposal for filtering gauge configurations by using adjoint zero modes. This method relies on the existence of the Supersymmetric Zero Mode (SZM), whose density follows the gauge action density for classical configurations. We review how a similar construction on the lattice is implemented based on the overlap operator and test the method against smooth configurations showing a remarkable agreement with the expected densities even when pairs of fractionals instanton/anti-instantons are present and noise is added. Then we explore the application of the method to Monte Carlo generated configurations based on SU(2) gauge group. The tuning of the parameters and quantitative results are explicitly shown for a $T^3\times R$ lattice. We show explicit examples comparing the AFM to the density obtained from the Gradient Flow. The agreement is remarkable for some specific configurations containing fractional instantons with the advantage that the AFM does not modify the underlying structures.

hep-lat↗

arXiv2023

Extracting Yang-Mills topological structures with adjoint modes

We report on how adjoint zero modes can be used to filter out the topological structures of gauge configurations from the UV fluctuations. We will use the Adjoint Filtering Method (AFM) which relies on the existence of a particular Supersymmetric Zero Mode (SZM) that follows closely the (anti)self-dual part of the action density. In contrast, it is not guaranteed that summing over the lowest lying modes in the fundamental representation reproduces the topological density. We present preliminary qualitative results on smooth, heated, and Monte-Carlo generated configurations with non-trivial content of fractional instantons. The method is capable of distinguishing the underlying topological structures without significantly modifying the gauge field as opposed to smoothing techniques. The method looks promising as a tool to investigate and extend recent studies based on semiclassical methods.

hep-lat↗

arXiv2023

The large-$N$ limit of the chiral condensate from twisted reduced models

We compute the large-$N$ limit of the QCD chiral condensate on the lattice using twisted reduced models, and performing controlled continuum and chiral extrapolations. We perform two different calculations: one consists in extracting the chiral condensate from the quark mass dependence of the pion mass, and the other consists in extracting the chiral condensate from the behaviour of the mode number of the Wilson-Dirac operator for small eigenvalues. We find consistency between the results of the two methods, giving a joint estimate of $\lim_{N\to\infty}Σ(N)/N=[184(13)$ MeV$]^3$ ($\overline{\mathrm{MS}}$, $μ=2$ GeV, taking the square root of the string tension $\sqrtσ=440$ MeV to set the scale), in remarkable agreement with the $\mathrm{SU}(3)$ 2-flavor FLAG result.

hep-lat↗

arXiv2023

The chiral condensate at large $N$

We present results for the large-$N$ limit of the chiral condensate computed from twisted reduced models. We followed a two-fold strategy, one constiting in extracting the condensate from the quark-mass dependence of the pion mass, the other consisting in extracting the condensate from the mode number of the Dirac operator.

hep-lat↗

arXiv2022

Perturbative study of large $N$ principal chiral model with twisted reduction

We compute the first four perturbative coefficients of the internal energy for the twisted reduced principal chiral model (TRPCM) using numerical stochastic perturbation theory (NSPT). This matrix model has the same large $N$ limit as the ordinary principal chiral model (PCM) at infinite volume. Indeed, we verify that the first three coefficients match the analytic result for the PCM coefficients at large $N$ with a precision of three to four significant digits. The fourth coefficient also matches our own NSPT calculation of the corresponding PCM coefficient at large $N$. The finite-$N$ corrections to all coefficients beyond the leading order are smaller for TRPCM than for PCM. We analyze the variance to determine the feasibility of extending the calculations to higher orders.

hep-lat↗

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

Towards higher order numerical stochastic perturbation computation applied to the twisted Eguchi-Kawai model

We have evaluated perturbation coefficients of Wilson loops up to $O(g^8)$ for the four-dimensional twisted Eguchi-Kawai model using the numerical stochastic perturbation theory (NSPT) in arXiv:1902.09847. In this talk we present a progress report on the higher order calculation up to $O(g^{63})$, for which we apply a fast Fourier transformation (FFT) based convolution algorithm to the multiplication of polynomial matrices in the NSPT aiming for higher order calculation. We compare two implementations with the CPU-only version and the GPU version of the FFT based convolution algorithm, and find a factor 9 improvement on the computational speed of the NSPT algorithm with SU($N=225$) at $O(g^{31})$. The perturbation order dependence of the computational time, we investigate it up to $O(g^{63})$, shows a mild scaling behavior on the truncation order.

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↗

arXiv2019

Constructing SU(N) fractional instantons

We study self-dual SU(N) gauge field configurations on the 4 torus with twisted boundary conditions, known as fractional instantons. Focusing on the minimum non-zero action case, we generalize the constant field strength solutions discovered by `t Hooft and valid for certain geometries. For the general case, we construct the vector potential and field strength in a power series expansion in a deformation parameter of the metric. The next to leading term is explicitly computed. The methodology is an extension of that used by the author for SU(2) fractional instantons and for vortices in two-dimensional Abelian Higgs models. Obviously, these solutions can also be seen as self-dual configurations in $\mathbb{R}^4$ having a crystal structure, where each node of the crystal carries a topological charge of $1/N$.

hep-th↗