arXiv subjects

Margarita Garcia Perez

Publications and source records attributed to Margarita Garcia Perez.

At least 19 recordsLinked to original sources

arXiv2022

SU(N) fractional Instantons

We present our study of a set of solutions to the $SU(N)$ Yang-Mills equations of motion with fractional topological charge. The configurations are obtained numerically by minimizing the action with gradient flow techniques on a torus of size $l^2\times(Nl)^2$ with twisted boundary conditions. We pay special attention to the large $N$ limit, which is taken along a very peculiar sequence, with the number of colors $N$ and the magnetic flux $m$ selected respectively as the $n$-th and $n-2$ terms of the Fibonacci sequence. We discuss the large $N$ scaling of the solutions and analyze several gauge invariant quantities as the Polyakov loops. We also discuss the so-called Hamiltonian limit, with one of the large directions sent to infinity, where these instantons represent tunneling events between inequivalent pure gauge configurations.

hep-th↗

arXiv2022

Scale setting for large-$N$ SUSY Yang-Mills on the lattice

In this paper we study the large $N$ limit of four-dimensional Supersymmetric Yang-Mills on the lattice using twisted reduced models. We have generated configurations with dynamical massive gluinos and various lattice 't Hooft couplings, and verified that the Pfaffian remains positive. We have determined the lattice spacing in terms of various observables obtaining compatible results. Extrapolating to the massless gluino limit we obtain the lattice spacing dependence on the bare couplings for the supersymmetric theory. The observed dependence goes along the expected behaviour predicted by perturbation theory.

hep-lat↗

arXiv2021

The SU(N) running coupling in the twisted gradient flow scheme and volume independence

We report on an ongoing study of the running coupling of SU(N) pure Yang-Mills theory in the twisted gradient flow scheme (TGF). The study exploits the idea that twisted boundary conditions reduce finite volume effects, leading to an effective size in the twisted plane that combines the number of colours and the torus period. We test this hypothesis by computing the TGF running coupling and the SU(N) $Λ-$ parameter on asymmetric lattices of size $(NL)^2L^2$ for various gauge groups. Finite volume effects are monitored by analyzing the coupling in different planes and by comparing results at different number of colours.

hep-lat↗

arXiv2021

Memory efficient finite volume schemes with twisted boundary conditions

In this paper we explore a finite volume renormalization scheme that combines three main ingredients: a coupling based on the gradient flow, the use of twisted boundary conditions and a particular asymmetric geometry, that for $SU(N)$ gauge theories consists on a hypercubic box of size $l^2 \times (Nl)^2$, a choice motivated by the study of volume independence in large $N$ gauge theories. We argue that this scheme has several advantages that make it particularly suited for precision determinations of the strong coupling, among them translational invariance, an analytic expansion in the coupling and a reduced memory footprint with respect to standard simulations on symmetric lattices, allowing for a more efficient use of current GPU clusters. We test this scheme numerically with a determination of the $Λ$ parameter in the $SU(3)$ pure gauge theory. We show that the use of an asymmetric geometry has no significant impact in the size of scaling violations, obtaining a value $Λ_{\overline{MS}} \sqrt{8 t_0} =0.603(17)$ in good agreement with the existing literature. The role of topology freezing, that is relevant for the determination of the coupling in this particular scheme and for large $N$ applications, is discussed in detail.

hep-lat↗

arXiv2020

Prospects for large N gauge theories on the lattice

I will review recent progress on addressing large N gauge theories on the lattice. The focus will be put on the use of large N volume independence as an effective tool to compute non-perturbative dynamics at, otherwise unreachable, large number of colours. A selection of results will be presented and future prospects and challenges for the study of large N QCD and various extensions will be discussed.

hep-lat↗

arXiv2020

The twisted gradient flow running coupling in SU(3): a non-perturbative determination

We report some preliminary results of our ongoing non-perturbative computation of the twisted 't Hooft running coupling in a particular set-up, using the gradient flow to define the coupling and step scaling techniques to compute it. For the computation we considered a pure gauge SU(3) theory in four dimensions, defined on the lattice on an asymmetrical torus endowed with twisted boundary conditions in a single plane, and related the energy scale of the coupling to an effective size combining the size of the torus and the rank of the gauge group. Additionally, we explore some of the effects of the freezing of the topology on the computation of the coupling.

hep-lat↗

arXiv2019

The twisted gradient flow coupling at one loop

We compute the one-loop running of the $SU(N)$ 't Hooft coupling in a finite volume gradient flow scheme using twisted boundary conditions. The coupling is defined in terms of the energy density of the gradient flow fields at a scale $\tilde{l}$ given by an adequate combination of the torus size and the rank of the gauge group, and is computed in the continuum using dimensional regularization. We present the strategy to regulate the divergences for a generic twist tensor, and determine the matching to the $\overline{\rm MS}$ scheme at one-loop order. For the particular case in which the twist tensor is non-trivial in a single plane, we evaluate the matching coefficient numerically and determine the ratio of $Λ$ parameters between the two schemes. We analyze the $N$ dependence of the results and the possible implications for non-commutative gauge theories and volume independence.

hep-lat↗

arXiv2018

The perturbative SU(N) one-loop running coupling in the twisted gradient flow scheme

We report on our computation of the perturbative running of the 't Hooft coupling in a pure gauge $SU(N)$ theory with twisted boundary conditions. The coupling is defined in terms of the energy density of the flow fields at a scale given by a particular combination of the linear size of the torus and the rank of the gauge group. We present our results for the matching at one-loop order to the $\bar{MS}$ scheme in the case of a two-dimensional non-trivial twist. The ratio of $Λ$ parameters is determined for the case of $SU(3)$ and for various other values of the number of colours and several choices of the magnetic flux induced by the twist.

hep-lat↗

arXiv2016

Volume reduction through perturbative Wilson loops

We derive the perturbative expansion of Wilson loops to order g^4 in a SU(N) lattice gauge theory with twisted boundary conditions. Our expressions show that the thermodynamic limit is attained at infinite N for any number of lattice sites and allow to quantify the deviations from volume independence at finite large N as a function of the twist.

hep-lat↗

arXiv2016

Perturbative running of the twisted Yang-Mills coupling in the gradient flow scheme

We report on our ongoing computation of the perturbative running of the Yang-Mills coupling using gradient flow techniques. In particular, we use the gradient flow method with twisted boundary conditions to perform a perturbative expansion of the expectation value of the Yang-Mills energy density up to fourth order in the coupling at finite flow time. We regularise the resulting integrals using dimensional regularisation, and reproduce the universal coefficient of the 1/ε term in the relation between bare and renormalised couplings. The computation of the finite part leading to a determination of the Λ parameter in this scheme is underway.

hep-lat↗

arXiv2014

Volume independence for Yang-Mills fields on the twisted torus

We review some recent results related to the notion of volume independence in SU(N) Yang-Mills theories. The topic is discussed in the context of gauge theories living on a d-dimensional torus with twisted boundary conditions. After a brief introduction reviewing the formalism for introducing gauge fields on a torus, we discuss how volume independence arises in perturbation theory. We show how, for appropriately chosen twist tensors, perturbative results to all orders in the 't Hooft coupling depend on a specific combination of the rank of the gauge group (N) and the periods of the torus (l) given by l N^{2/d}, for d even.We discuss the well-known relation to non-commutative field theories and address certain threats to volume independence associated to the occurrence of tachyonic instabilities at one-loop order. We end by presenting some numerical results in 2+1 dimensions that extend these ideas to the non-perturbative domain.

hep-th↗

arXiv2013

Perturbative analysis of twisted volume reduced theories

We discuss the perturbative expansion of SU(N) Yang-Mills theories defined on a d-dimensional torus of linear size l with twisted boundary conditions, generalizing previous results in the literature. For a specific class of twist tensors depending on a single integer flux value k, we show that perturbative results to all orders depend on the combination lN^(2/d) and a flux-dependent angle theta. This implies a new kind of volume independence that holds at finite N and for fixed values of theta. Our results also provide interesting information about the possible occurrence of tachyonic instabilities at one-loop order. We support the prescription that instabilities are avoided, if the large N limit is taken keeping theta > theta_c, and appropriately scaling the magnetic flux k with N. Numerical results in 2+1 dimensions provide a test of how these ideas extend into the non-perturbative regime.

hep-lat↗

arXiv2013

Mass anomalous dimension from large N 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. Taking advantage of large N twisted volume reduction we do this on a single site lattice, but we should still get infinite-volume physics in the large N limit. We describe our progress in extracting the mass anomalous dimension from the eigenvalue distribution of the adjoint Dirac operator, using data for N up to 289.

hep-lat↗

arXiv2012

Volume dependence in 2+1 Yang-Mills theory

We present the results of an analysis of a 2+1 dimensional pure SU(N) Yang-Mills theory formulated on a 2-dimensional spatial torus with non-trivial magnetic flux. We focus on investigating the dependence of the electric-flux spectrum, extracted from Polyakov loop correlators, with the spatial size l, the number of colours N, and the magnetic flux m. The size of the torus acts a parameter that allows to control the onset of non-perturbative effects. In the small volume regime, where perturbation theory holds, we derive the one-loop self-energy correction to the single-gluon spectrum, for arbitrary N and m. We discuss the transition from small to large volumes that has been investigated by means of Monte-Carlo simulations. We argue that the energy of electric flux e, for the lowest gluon momentum, depends solely on e/N and on the dimensionless variable x=lambda N l, with lambda the 't Hooft coupling. The variable x can be interpreted as the dimensionless 't Hooft coupling for an effective box size given by Nl. This implies a version of reduction that allows to trade l by N without modifying the electric-flux energy.

hep-lat↗

arXiv2011

Ultraviolet filtering of lattice configurations and applications to Monte Carlo dynamics

We present a detailed study of a filtering method based upon Dirac quasi-zero-modes in the adjoint representation. The procedure induces no distortions on configurations which are solutions of the euclidean classical equations of motion. On the other hand, it is very effective in reducing the short-wavelength stochastic noise present in Monte Carlo generated configurations. After testing the performance of the method in various situations, we apply it successfully to study the effect of Monte Carlo dynamics on topological structures like instantons.

hep-lat↗

arXiv2010

From confinement to adjoint zero-modes

Starting from our proposed model of the Yang-Mills vacuum based on fractional instantons, we review the intellectual itinerary which has guided part of our scientific activity up to our recent work on adjoint zero-modes for calorons.

hep-th↗

arXiv2008

Gluino zero-modes for calorons at finite temperature

We study the solutions of the Dirac equation in the adjoint representation(gluinos) in the background field of SU(2) unit charge calorons. Our solutions are forced to be antiperiodic in thermal time and would occur naturally in a semiclassical approach to N=1 Super-symmetric Yang-Mills theory at finite temperature.

hep-th↗

arXiv2008

Primordial magnetic fields from preheating at the electroweak scale

We analyze the generation of helical magnetic fields during preheating in a model of low-scale electroweak (EW) hybrid inflation. We show how the inhomogeneities in the Higgs field, resulting from tachyonic preheating after inflation, seed the magnetic fields in a way analogous to that predicted by Vachaspati and Cornwall in the context of the EW symmetry breaking. At this stage, the helical nature of the generated magnetic fields is linked to the non-trivial winding of the Higgs-field. We analyze non-perturbatively the evolution of these helical seeds through the highly non-linear stages of symmetry breaking (SB) and beyond. Electroweak SB occurs via the nucleation and growth of Higgs bubbles which squeeze the magnetic fields into string-like structures. The W-boson charge density clusters in lumps around the magnetic strings. After symmetry breaking, a detailed analysis of the magnetic field Fourier spectrum shows two well differentiated components: a UV radiation tail at a temperature T ~ 0.23 m_higgs slowly growing with time, and an IR peak associated to the helical magnetic fields, which seems to follow inverse cascade. The system enters a regime in which we observe that both the amplitude (ρ_B/ρ_{EW} ~ 0.01) and the correlation length of the magnetic field grow linearly with time. During this stage of evolution we also observe a power-law growth in the helical susceptibility. These properties support the possibility that our scenario could provide the seeds eventually evolving into the microgauss fields observed today in galaxies and clusters of galaxies.

hep-ph↗