Abstract: The recent introduction of machine learning techniques, especially normalizing flows, for the sampling of lattice gauge theories has shed some hope on improving the sampling efficiency of the traditional hybrid Monte Carlo (HMC) algorithm. In this work we study a modified HMC algorithm that draws on the seminal work on trivializing flows by L & uuml;scher. Autocorrelations are reduced by sampling from a simpler action that is related to the original action by an invertible mapping realised through Normalizing Flows models with a minimal set of training parameters. We test the algorithm in a f(4) theory in 2D where we observe reduced autocorrelation times compared with HMC, and demonstrate that the training can be done at small unphysical volumes and used in physical conditions. We also study the scaling of the algorithm towards the continuum limit under various assumptions on the network architecture.

Abstract: 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) x (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 A 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 Lambda((MS) over bar)root 8t(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.

Abstract: Gauge theories with matter fields in various representations play an important role in different branches of physics. Recently, it was proposed that several aspects of the pseudogap phase of cuprate superconductors near optimal doping may be explained by an emergent SU(2) gauge symmetry. Around the transition with positive hole doping, one can construct a (2 + 1)-dimensional SU(2) gauge theory coupled to four adjoint scalar fields which gives rise to a rich phase diagram with a myriad of phases having different broken symmetries. We study the phase diagram of this model on the Euclidean lattice using the hybrid Monte Carlo algorithm. We find the existence of multiple broken phases as predicted by previous mean-field studies. Depending on the quartic couplings, the SU(2) gauge symmetry is broken down either to U(1) or Z2 in the perturbative description of the model. We further study the confinement-deconfinement transition in this theory, and find that both the broken phases are deconfining in the range of volumes that we studied. However, there exists a marked difference in the behavior of the Polyakov loop between the two phases.

Abstract: Monte Carlo methods represent a cornerstone of computer science. They allow sampling high dimensional distribution functions in an efficient way. In this paper we consider the extension of Automatic Differentiation (AD) techniques to Monte Carlo processes, addressing the problem of obtaining derivatives (and in general, the Taylor series) of expectation values. Borrowing ideas from the lattice field theory community, we examine two approaches. One is based on reweighting while the other represents an extension of the Hamiltonian approach typically used by the Hybrid Monte Carlo (HMC) and similar algorithms. We show that the Hamiltonian approach can be understood as a change of variables of the reweighting approach, resulting in much reduced variances of the coefficients of the Taylor series. This work opens the door to finding other variance reduction techniques for derivatives of expectation values.

Abstract: Lattice QCD has reached a mature status. State of the art lattice computations include u, d, s (and even the c) sea quark effects, together with an estimate of electromagnetic and isospin breaking corrections for hadronic observables. This precise and first principles description of the standard model at low energies allows the determination of multiple quantities that are essential inputs for phenomenology and not accessible to perturbation theory. One of the fundamental parameters that are determined from simulations of lattice QCD is the strong coupling constant, which plays a central role in the quest for precision at the LHC. Lattice calculations currently provide its best determinations, and will play a central role in future phenomenological studies. For this reason we believe that it is timely to provide a pedagogical introduction to the lattice determinations of the strong coupling. Rather than analysing individual studies, the emphasis will be on the methodologies and the systematic errors that arise in these determinations. We hope that these notes will help lattice practitioners, and QCD phenomenologists at large, by providing a self-contained introduction to the methodology and the possible sources of systematic error. The limiting factors in the determination of the strong coupling turn out to be different from the ones that limit other lattice precision observables. We hope to collect enough information here to allow the reader to appreciate the challenges that arise in order to improve further our knowledge of a quantity that is crucial for LHC phenomenology. Crown Copyright & nbsp;(c) 2021 Published by Elsevier B.V. All rights reserved.