arXiv subjects

Biagio Lucini

Publications and source records attributed to Biagio Lucini.

At least 37 records · Page 2Linked to original sources

arXiv2025

Topological Data Analysis of Abelian Magnetic Monopoles in Gauge Theories

Motivated by recent literature on the possible existence of a second higher-temperature phase transition in Quantum Chromodynamics, we revisit the proposal that colour confinement is related to the dynamics of magnetic monopoles using methods of Topological Data Analysis, which provides a mathematically rigorous characterisation of topological properties of quantities defined on a lattice. After introducing persistent homology, one of the main tools in Topological Data Analysis, we shall discuss how this concept can be used to quantitatively analyse the behaviour of monopoles across the deconfinement phase transition. Our approach is first demonstrated for Compact $U(1)$ Lattice Gauge Theory, which is known to have a zero-temperature deconfinement phase transition driven by the restoration of the symmetry associated with the conservation of the magnetic charge. For this system, we perform a finite-size scaling analysis of observables capturing the homology of magnetic current loops, showing that the expected value of the deconfinement critical coupling is reproduced by our analysis. We then extend our method to $SU(3)$ gauge theory, in which Abelian magnetic monopoles are identified after projection in the Maximal Abelian Gauge. A finite-size scaling of our homological observables of Abelian magnetic current loops at temporal size $N_t = 4$ provides the expected value of the critical coupling with an accuracy that is generally higher than that obtained with conventional thermodynamic approaches at comparable statistics, hinting towards the relevance of topological properties of monopole currents for confinement.

hep-lat↗

arXiv2024

Random Matrix Theory for Stochastic Gradient Descent

Investigating the dynamics of learning in machine learning algorithms is of paramount importance for understanding how and why an approach may be successful. The tools of physics and statistics provide a robust setting for such investigations. Here we apply concepts from random matrix theory to describe stochastic weight matrix dynamics, using the framework of Dyson Brownian motion. We derive the linear scaling rule between the learning rate (step size) and the batch size, and identify universal and non-universal aspects of weight matrix dynamics. We test our findings in the (near-)solvable case of the Gaussian Restricted Boltzmann Machine and in a linear one-hidden-layer neural network.

hep-lat↗

arXiv2024

Stochastic weight matrix dynamics during learning and Dyson Brownian motion

We demonstrate that the update of weight matrices in learning algorithms can be described in the framework of Dyson Brownian motion, thereby inheriting many features of random matrix theory. We relate the level of stochasticity to the ratio of the learning rate and the mini-batch size, providing more robust evidence to a previously conjectured scaling relationship. We discuss universal and non-universal features in the resulting Coulomb gas distribution and identify the Wigner surmise and Wigner semicircle explicitly in a teacher-student model and in the (near-)solvable case of the Gaussian restricted Boltzmann machine.

cond-mat.dis-nn↗

arXiv2024

Progress on the spectroscopy of an Sp(4) gauge theory coupled to matter in multiple representations

We report progress on our lattice calculations for the mass spectra of low-lying composite states in the Sp(4) gauge theory coupled to two and three flavors of Dirac fermions transforming in the fundamental and the two-index antisymmetric representations, respectively. This theory provides an ultraviolet completion to the composite Higgs model with Goldstone modes in the SU(4)/Sp(4) coset and with partial compositeness for generating the top-quark mass. We measure the meson and chimera baryon masses. These masses are crucial for constructing the composite Higgs model. In particular, the chimera baryon masses are important inputs for implementing top partial compositeness. We employ Wilson fermions and the Wilson plaquette action in our simulations. Techniques such as APE and Wuppertal smearing, as well as the procedure of generalised eigenvalue problem, are implemented in our analysis.

hep-lat↗

arXiv2024

Updates on the density of states method in finite temperature symplectic gauge theories

First-order phase transitions in the early universe have rich phenomenological implications, such as the production of a potentially detectable signal of stochastic relic background gravitational waves. The hypothesis that new, strongly coupled dynamics, hiding in a new dark sector, could be detected in this way, via the telltale signs of its confinement/deconfinement phase transition, provides a fascinating opportunity for interdisciplinary synergy between lattice field theory and astro-particle physics. But its viability relies on completing the challenging task of providing accurate theoretical predictions for the parameters characterising the strongly coupled theory. Density of states methods, and in particular the linear logarithmic relaxation (LLR) method, can be used to address the intrinsic numerical difficulties that arise due the meta-stable dynamics in the vicinity of the critical point. For example, it allows one to obtain accurate determinations of thermodynamic observables that are otherwise inaccessible, such as the free energy. In this contribution, we present an update on results of the analysis of the finite temperature deconfinement phase transition in a pure gauge theory with a symplectic gauge group, $Sp(4)$, by using the LLR method. We present a first analysis of the properties of the transition in the thermodynamic limit, and provide a road map for future work, including a brief preliminary discussion that will inform future publications.

hep-lat↗

arXiv2024

Dyson Brownian motion and random matrix dynamics of weight matrices during learning

During training, weight matrices in machine learning architectures are updated using stochastic gradient descent or variations thereof. In this contribution we employ concepts of random matrix theory to analyse the resulting stochastic matrix dynamics. We first demonstrate that the dynamics can generically be described using Dyson Brownian motion, leading to e.g. eigenvalue repulsion. The level of stochasticity is shown to depend on the ratio of the learning rate and the mini-batch size, explaining the empirically observed linear scaling rule. We verify this linear scaling in the restricted Boltzmann machine. Subsequently we study weight matrix dynamics in transformers (a nano-GPT), following the evolution from a Marchenko-Pastur distribution for eigenvalues at initialisation to a combination with additional structure at the end of learning.

cond-mat.dis-nn↗

arXiv2024

Towards the $β$ function of SU(2) with adjoint matter using Pauli-Villars fields

The family of SU(2) theories with matter transforming in the adjoint representation has attracted interest from many angles. The two-flavour theory, known as Minimal Walking Technicolor, has a body of evidence pointing to it being in the conformal window with anomalous dimension $γ_{*}\approx0.3$. Perturbative calculations would suggest that the one-flavour theory should be confining and chirally broken; however, lattice studies of the theory have been inconclusive. In this contribution we present a first look at efforts towards the computation of the beta function of these theories using the gradient flow methodology. Following an exploration of the phase diagram of the two theories with Wilson fermions and additional Pauli-Villars fields, we tune the bare fermion mass to near the chiral limit, and subsequently generate ensembles at five lattice volumes and a range of lattice spacings.

hep-lat↗

arXiv2024

Progress on the spectroscopy of lattice gauge theories using spectral densities

Spectral densities encode non-perturbative information crucial in computing physical observables in strongly coupled field theories. Using lattice gauge theory data, we perform a systematic study to demonstrate the potential of recent technological advances in the reconstruction of spectral densities. We develop, maintain and make publicly available dedicated analysis code that can be used for broad classes of lattice theories. As a test case, we analyse the Sp(4) gauge theory coupled to an admixture of fermions transforming in the fundamental and two-index antisymmetric representations. We measure the masses of mesons in energy-smeared spectral densities, after optimising the smearing parameters for available lattice ensembles. We present a summary of the mesons mass spectrum in all the twelve (flavored) channels available, including also several excited states.

hep-lat↗

arXiv2024

Progress on pseudoscalar flavour-singlets in Sp(4) with mixed fermion representations

We measure the masses of the pseudoscalar flavour-singlet meson states in the $Sp(4)$ gauge theory coupled to two Dirac fermions transforming in the fundamental representation and three Dirac fermions in the antisymmetric representation. This theory provides a compelling ultraviolet completion for the minimal composite Higgs model implementing also partial compositeness for the top quark. The spectrum contains two, comparatively light, pseudoscalar flavour-singlet states, which mix with one another. One of them is a Nambu-Goldstone boson (in the massless limit), whereas the other receives a mass from the $U(1)_A$ axial anomaly. We demonstrate how to measure the mixing between these two states. For moderately heavy fermion masses, we find that the two wave functions are dominated by one of the fermion representations, mixing effects being small.

hep-lat↗

arXiv2024

Mixing between flavor singlets in lattice gauge theories coupled to matter fields in multiple representations

We provide the first extensive, numerical study of the non-trivial problem of mixing between flavor-singlet composite states emerging in strongly coupled lattice field theories with matter field content consisting of fermions transforming in different representations of the gauge group. The theory of interest is the minimal candidate for a composite Higgs model that also accommodates a mechanism for top partial compositeness: the $Sp(4)$ gauge theory coupled to two (Dirac) fermions transforming as the fundamental and three as the two-index antisymmetric representation of the gauge group, respectively. We apply an admixture of APE and Wuppertal smearings, as well as the generalized eigenvalue problem approach, to two-point functions involving flavor-singlet mesons, for ensembles having time extent longer than the space extent. We demonstrate that, in the region of lattice parameter space accessible to this study, both masses and mixing angles can be measured effectively, despite the presence of (numerically noisy) contributions from disconnected diagrams.

hep-lat↗

arXiv2024

Meson spectroscopy from spectral densities in lattice gauge theories

Spectral densities encode non-perturbative information that enters the calculation of a plethora of physical observables in strongly coupled field theories. Phenomenological applications encompass aspects of standard-model hadronic physics, observable at current colliders, as well as correlation functions characterizing new physics proposals, testable in future experiments. By making use of numerical data produced in a Sp(4) lattice gauge theory with matter transforming in an admixture of fundamental and 2-index antisymmetric representations of the gauge group, we perform a systematic study to demonstrate the effectiveness of recent technological progress in the reconstruction of spectral densities. To this purpose, we write and test new software packages that use energy-smeared spectral densities to analyze the mass spectrum of mesons. We assess the effectiveness of different smearing kernels and optimize the smearing parameters to the characteristics of available lattice ensembles. We generate new ensembles for the theory in consideration, with lattices that have a longer extent in the time direction with respect to the spatial ones. We run our tests on these ensembles, obtaining new results about the spectrum of light mesons and their excitations. We make available our algorithm and software for the extraction of spectral densities, that can be applied to theories with other gauge groups, including the theory of strong interactions (QCD) governing hadronic physics in the standard model.

hep-lat↗

arXiv2024

Topological Data Analysis of Monopole Current Networks in $U(1)$ Lattice Gauge Theory

In $4$-dimensional pure compact $U(1)$ lattice gauge theory, we analyse topological aspects of the dynamics of monopoles across the deconfinement phase transition. We do this using tools from Topological Data Analysis (TDA). We demonstrate that observables constructed from the zeroth and first homology groups of monopole current networks may be used to quantitatively and robustly locate the critical inverse coupling $β_{c}$ through finite-size scaling. Our method provides a mathematically robust framework for the characterisation of topological invariants related to monopole currents, putting on firmer ground earlier investigations. Moreover, our approach can be generalised to the study of Abelian monopoles in non-Abelian gauge theories.

hep-lat↗

arXiv2024

On the spectrum of mesons in quenched $Sp(2N)$ gauge theories

We report the findings of our extensive study of the spectra of flavoured mesons in lattice gauge theories with symplectic gauge group and fermion matter content treated in the quenched approximation. For the $Sp(4)$, $Sp(6)$, and $Sp(8)$ gauge groups, the (Dirac) fermions transform in either the fundamental, or the 2-index, antisymmetric or symmetric, representations. This study sets the stage for future precision calculations with dynamical fermions in the low mass region of lattice parameter space. Our results have potential phenomenological applications ranging from composite Higgs models, to top (partial) compositeness, to dark matter models with composite, strong-coupling dynamical origin. Having adopted the Wilson flow as a scale-setting procedure, we apply Wilson chiral perturbation theory to extract the continuum and massless limits for the observables of interest. The resulting measurements are used to perform a simplified extrapolation to the large-$N$ limit, hence drawing a preliminary connection with gauge theories with unitary groups. We conclude with a brief discussion of the Weinberg sum rules.

hep-lat↗

arXiv2024

Lattice investigations of the chimera baryon spectrum in the Sp(4) gauge theory

We report the results of lattice numerical studies of the Sp(4) gauge theory coupled to fermions (hyperquarks) transforming in the fundamental and two-index antisymmetric representations of the gauge group. This strongly-coupled theory is the minimal candidate for the ultraviolet completion of composite Higgs models that facilitate the mechanism of partial compositeness for generating the top-quark mass. We measure the spectrum of the low-lying, half-integer spin, bound states composed of two fundamental and one antisymmetric hyperquarks, dubbed chimera baryons, in the quenched approximation. In this first systematic, non-perturbative study, we focus on the three lightest parity-even chimera-baryon states, in analogy with QCD, denoted as $Λ_{\rm CB}$, $Σ_{\rm CB}$ (both with spin 1/2), and $Σ_{\rm CB}^\ast$(with spin 3/2). The spin-1/2 such states are candidates of the top partners. The extrapolation of our results to the continuum and massless-hyperquark limit is performed using formulae inspired by QCD heavy-baryon Wilson chiral perturbation theory. Within the range of hyperquark masses in our simulations, we find that $Σ_{\mathrm{CB}}$ is not heavier than $Λ_{\mathrm{CB}}$.

hep-lat↗

arXiv2024

Scalar field Restricted Boltzmann Machine as an ultraviolet regulator

Restricted Boltzmann Machines (RBMs) are well-known tools used in Machine Learning to learn probability distribution functions from data. We analyse RBMs with scalar fields on the nodes from the perspective of lattice field theory. Starting with the simplest case of Gaussian fields, we show that the RBM acts as an ultraviolet regulator, with the cutoff determined by either the number of hidden nodes or a model mass parameter. We verify these ideas in the scalar field case, where the target distribution is known, and explore implications for cases where it is not known using the MNIST data set. We also demonstrate that infrared modes are learnt quickest.

hep-lat↗

arXiv2024

Chimera baryon spectrum in the Sp(4) completion of composite Higgs models

In strongly coupled gauge theories that serve as completions of composite Higgs models, the fermionic bound states formed by fermions (hyperquarks) transforming in different representations, called chimera baryons, could serve as top partners, by embedding of the Standard Model appropriately. We report our results on the spectrum of chimera baryons in the Sp(4) gauge theory with hyperquarks transforming in fundamental and two-index antisymmetric representations. For this study, we adopt the quenched approximation. We investigate the mass hierarchy between the lightest chimera baryons with different quantum numbers, as a function of the lattice parameters. Inspired by baryon chiral effective field theory, and the Akaike Information Criterion, we perform a first extrapolation to the continuum and massless-hyperquark limit.

hep-lat↗

arXiv2023

Singlets in gauge theories with fundamental matter

We provide the first determination of the mass of the lightest flavor-singlet pseudoscalar and scalar bound states (mesons), in the $\rm{Sp}(4)$ Yang-Mills theory coupled to two flavors of fundamental fermions, using lattice methods. This theory has applications both to composite Higgs and strongly-interacting dark matter scenarios. We find the singlets to have masses comparable to those of the light flavored states, which might have important implications for phenomenological models. We focus on regions of parameter space corresponding to a moderately heavy mass regime for the fermions. We compare the spectra we computed to existing and new results for $\rm{SU}(2)$ and $\rm{SU}(3)$ theories, uncovering an intriguing degree of commonality. As a by-product, in order to perform the aforementioned measurements, we implemented and tested, in the context of symplectic lattice gauge theories, several strategies for the treatment of disconnected-diagram contributions to two-point correlation functions. These technical advances set the stage for future studies of the singlet sector in broader portions of parameter space of this and other lattice theories with a symplectic gauge group.

hep-lat↗

arXiv2023

Symplectic lattice gauge theories on Grid: approaching the conformal window

Symplectic gauge theories coupled to matter fields lead to symmetry enhancement phenomena that have potential applications in such diverse contexts as composite Higgs, top partial compositeness, strongly interacting dark matter, and dilaton-Higgs models. These theories are also interesting on theoretical grounds, for example in reference to the approach to the large-N limit. A particularly compelling research aim is the determination of the extent of the conformal window in gauge theories with symplectic groups coupled to matter, for different groups and for field content consisting of fermions transforming in different representations. Such determination would have far-reaching implications, but requires overcoming huge technical challenges. Numerical studies based on lattice field theory can provide the quantitative information necessary to this endeavour. We developed new software to implement symplectic groups in the Monte Carlo algorithms within the Grid framework. In this paper, we focus most of our attention on the Sp(4) lattice gauge theory coupled to four (Wilson-Dirac) fermions transforming in the 2-index antisymmetric representation, as a case study. We discuss an extensive catalogue of technical tests of the algorithms and present preliminary measurements to set the stage for future large-scale numerical investigations. We also include the scan of parameter space of all asymptotically free Sp(4) lattice gauge theories coupled to varying number of fermions transforming in the antisymmetric representation.

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