arXiv subjects

Marco Frasca

Publications and source records attributed to Marco Frasca.

At least 19 recordsLinked to original sources

arXiv2026

Exact Lattice Identities and Continuum-Limit Dyson--Schwinger Equations for Yang-Mills Theory

Starting from SU(N) on the lattice, we give a rigorous derivation of the Dyson--Schwinger equations in the continuum limit. We formulate the Dyson--Schwinger identities for the lattice Yang--Mills theory directly in terms of the link variables $U_\mu(m)\in SU(N)$, exploiting the invariance of the Haar measure under left group translations. This provides an exact lattice derivation of the corresponding master equation for the Wilson action, expressed through left-invariant Lie derivatives acting on individual links. Because the construction is carried out directly on the compact gauge group, it avoids the ambiguities associated with introducing Lie-algebra valued gauge potentials as primary integration variables at finite lattice spacing. For practical applications, in a second part we then break down the gauge degree of freedom by choosing Feynman gauge. We analyze the continuum-limit form of the resulting lattice identities and derive equations for the one- and two-point connected functions. Under a further simplifying reduction, these equations close to a tractable scalar system. Our results establish a direct bridge between exact lattice identities and the functional equations commonly used in continuum nonperturbative studies of Yang--Mills theory.

hep-th↗

arXiv2026

Review of strongly coupled regimes in gravity with Dyson-Schwinger approach

We analyze various gravity theories involving de-Sitter, quadratic $\mathcal{R}^2$ and non-minimally coupled scalar in the light of application of the Dyson-Schwinger technique involving exact background solution of the Green's function. We denote specific set of solutions for the metric to move towards a quantum analysis of the theory. This kind of solutions is identified as conformally flat metric. Such a conclusion naturally arises in the use of the Dyson-Schwinger equations in the study of the Yang-Mills theory through the mapping theorem. We show a sequence of cosmological phase transitions starting from the breaking of such conformal invariance that can be hindered by the presence of the non-minimal coupling.

gr-qc↗

arXiv2026

Discrete Dyson-Schwinger equations

We develop the discrete set of Dyson-Schwinger equations for scalar fields and solve them for some cases. We show that their solutions are Gaussian in the continuum limit as expected from the theorems of Aizenman and of Aizenman and Duminil-Copin for $d\ge 4$. Extension to lower dimensionality fails, as it should, by observing that the triviality theorems used in our proof are not applicable in such cases.

math-ph↗

arXiv2026

Quantization-Aware Regularizers for Deep Neural Networks Compression

Deep Neural Networks reached state-of-the-art performance across numerous domains, but this progress has come at the cost of increasingly large and over-parameterized models, posing serious challenges for deployment on resource-constrained devices. As a result, model compression has become essential, and -- among compression techniques -- weight quantization is largely used and particularly effective, yet it typically introduces a non-negligible accuracy drop. However, it is usually applied to already trained models, without influencing how the parameter space is explored during the learning phase. In contrast, we introduce per-layer regularization terms that drive weights to naturally form clusters during training, integrating quantization awareness directly into the optimization process. This reduces the accuracy loss typically associated with quantization methods while preserving their compression potential. Furthermore, in our framework quantization representatives become network parameters, marking, to the best of our knowledge, the first approach to embed quantization parameters directly into the backpropagation procedure. Experiments on CIFAR-10 with AlexNet and VGG16 models confirm the effectiveness of the proposed strategy.

cs.LG↗

arXiv2025

Quintessence Dark Energy from non-perturbative Higgs-Yang-Mills mass gap

We discuss the equations that arise from a Higgs--Yang-Mills dark sector coupled to gravity on a flat Friedmann-Lemaitre-Robinson-Walker metric. We choose the simplest $SU(2)$ representation, which we show to be compatible with the Cosmological Principle. We devise a multiple time scale approach to solve the equations of motion through a hierarchy of the couplings, utilizing exact solutions in terms of Jacobi elliptic functions. This novel method implements the dynamical system approach used in the literature and can shed new light on the possibility that this model can describe dark energy.

astro-ph.CO↗

arXiv2025

Finite temperature QCD crossover at non-zero chemical potential: A Dyson-Schwinger approach

We study QCD at finite temperature and non-zero chemical potential to derive the critical temperature at the chiral phase transition (crossover). We solve a set of Dyson--Schwinger partial differential equations using the exact solution for the Yang--Mills quantum field theory based on elliptical functions. We derive a Nambu-Jona--Lasino (NJL) model of the quarks and obtain a very good agreement with recent lattice computations regarding the dependence of the critical temperature on the strong coupling scale. The solution depends on a single scale parameter, as typical for the theory and already known from studies about asymptotic freedom. The study is analytically derived from QCD.

hep-ph↗

arXiv2025

Mass gap in non-perturbative quadratic $\mathcal{R}^2$ gravity via Dyson-Schwinger

We apply in a simple model derived from quadratic $\mathcal{R}^2$ gravity the technique of Dyson-Schwinger equations to solve for its corresponding quantum theory. Particularly, we solve the classical equations of motion to get a solution to the hierarchy of Dyson-Schwinger equations in the limit of large Ricci scalar, assumed to be constant and larger than the square of the Starobinsky mass. Moving to the Einstein frame, the model admits Higgs-like solutions with a single particle having a finite mass. We quantize the scalar field showing the appearing of a mass gap through a Higgs-like solution. The presence of the mass gap, that increases with the square root of the Ricci scalar, shows how the effect of the scalar sector at low-energy becomes ineffective, making it relevant only at short distances.

hep-th↗

arXiv2024

Non-perturbative Origin of the Electroweak Scale with Dyson-Schwinger: Fermionic Mass Gap and Higher-order Excitations

We study interaction of a fermion field $\psi$ with a scalar field $\phi$ and analyze the spectrum of the theory obtained in this way. It is shown that due to non-perturbative dynamics in the hidden fermion sector, $\phi$ develops a vacuum expectation value (vev) in the form of a mass gap which triggers the electroweak symmetry breaking (EWSB) and dynamically generates the SM Higgs boson mass. For estimating the non-perturbatively generated mass scale, we solve the hierarchy of Dyson-Schwinger Equations in form of partial differential equations using the exact solution known via a novel technique developed by Bender, Milton and Savage. We employ Jacobi Elliptic function as exact background solution and show that the mass gap that arises in the fermion sector can be transmuted to the EW sector, expressed in terms of fermion mass and the $\phi$ self-quartic. We identify the suitable parameter space where the observed SM Higgs boson can be successfully generated .

hep-ph↗

arXiv2024

Non-perturbative Origin of Electroweak Scale via Higgs-portal: Dyson-Schwinger in Conformally Invariant Scalar Sector

We investigate conformally extended Standard Model with a hidden scalar $\phi$. It is shown that due to non-perturbative dynamics in the hidden sector, $\phi$ develops a vacuum expectation value (vev) in the form of a mass gap which triggers the electroweak symmetry breaking (EWSB) and dynamically generates the SM Higgs boson mass. For estimating the non-perturbatively generated mass scale, we solve the hierarchy of Dyson-Schwinger Equations in form of partial differential equations using the exact solution known via a novel technique developed by Bender, Milton and Savage. We employ Jacobi Elliptic function as exact background solution and show that the mass gap that arises in the hidden sector can be transmuted to the EW sector, expressed in terms of Higgs-portal mixed quartic coupling $\beta$ and self interaction quartic coupling $\lambda_{\phi}$ of $\phi$. We identify the suitable parameter space where the observed SM Higgs boson can be successfully generated . Finally, we discuss how this idea of non-perturbative EW scale generation can serve as a new starting point for better realistic model building in the context of resolving the hierarchy problem in the Standard Model.

hep-ph↗

arXiv2024

Dynamical generation of electroweak scale from the conformal sector: A strongly coupled Higgs via the Dyson--Schwinger approach

We propose a novel pathway to generate the electroweak (EW) scale via non-perturbative dynamics of a conformally invariant scalar sector at the classical level. We provide a method to estimate the non-perturbative EW scale generation using the exact solution of the background equations of motion in a scalar theory via the Dyson-Schwinger approach. Particularly, we find an analytical result for the Higgs mass in the strongly coupled regime in terms of its quartic self interaction term and the cut-off scale of the theory. We also show that the Higgs sector is an essential part of the Standard Model as, without it, a Yang--Mills gauge theory cannot acquire mass even if a self-interaction term is present. Our analysis lead to a more realistic model building with possible solutions to the gauge hierarchy problem and, in general, to the dynamical generation of any scales scales in nature, be it the visible sector or the dark sector.

hep-ph↗

arXiv2024

Phenomenological Aspects of Lee-Wick QED

We study some phenomenological aspects of Lee-Wick (LW) QED. In particular, we show that LW QED implies charge dequantization and a flavor-dependent LW scale. We study the implications of the Weak Gravity Conjecture (WGC) in LW QED and calculate the modified electric force and potential and use the former to reformulate the WGC in LW QED. We also calculate the photon self-energy and the Uehling potential in LW QED. We show that bounds on milli-charged particles from matter neutrality experiments and from Cavendish-type experiments set stringent limits on the LW scale of fermions and of the photon.

hep-ph↗

arXiv2024

Non-perturbative Origin of the Electroweak Scale: RGE in Strongly-coupled Dark Gauge Theories via Dyson-Schwinger

We propose a novel pathway to generate the electroweak scale (EW) via non-perturbative dynamics of a dark gauge sector based on the SU(N) gauge group. Imposing the scale invariance of the theory, we investigate the electroweak symmetry breaking (EWSB) which is triggered dynamically via the condensation of gauge fields. Instead of the usual dimension-4 triggered breaking, a dimension 6 term (with Wilson coefficient compatible with SMEFT bounds) coupling the Higgs boson and the Yang-Mills field quadratic term in the Lagrangian provides feedback from the gauge to the Higgs sector. We provide a novel method to estimate a non-perturbative EW scale generation using the exact solution of a truncated set of the background equations of motion in Yang-Mills theory in terms of Jacobi elliptic functions and the exact beta-function valid in the strongly coupled regimes via the Dyson-Schwinger approach. Particularly, we find an analytical result for the Renormalization Group Equation (RGE) of the gauge coupling in the $SU(N)$ sector in the strongly-coupled regime. The dynamics studied in this paper pave the way to a more realistic model building with possible resolution to the hierarchy problem and, in general, dynamical generation of scales.

hep-ph↗

arXiv2023

Some exact Green function solutions for non-linear classical field theories

We consider some non-linear non-homogeneous partial differential equations (PDEs) and derive their exact Green function solution as a functional Taylor expansion in powers of the source. The kind of PDEs we consider are dispersive ones where the exact solution of the corresponding homogeneous equations can have some known shape. The technique has a formal similarity with the Dyson--Schwinger set of equations to solve quantum field theories. However, there are no physical constraints. Indeed, we show that a complete coincidence with the statistical field model of a quartic scalar theory can be achieved in the Gaussian expansion of the cumulants of the partition function.

math-ph↗

arXiv2023

Non-perturbative quantum Yang--Mills at finite temperature beyond lattice: a Dyson--Schwinger approach

Using a Dyson--Schwinger approach, we perform an analysis of the non-trivial ground state of thermal $SU(N)$ Yang--Mills theory in the non-perturbative regime where chiral symmetry is dynamically broken by a mass gap. Basic thermodynamic observables such as energy density and pressure are derived analytically, using Jacobi elliptic functions. The results are compared with lattice results. Good agreement is found at low temperatures, providing a viable scenario of a gas of massive glue states populating higher levels of the spectrum of the theory. At high temperatures a scenario without glue states consistent with a massive scalar field is observed, showing an interesting agreement with lattice data. The possibility is discussed that the results derived in this analysis open up a novel pathway beyond lattice to precision studies of phase transitions with false vacuum and cosmological relics that depend on the equations of state in strong coupled gauge theories of the type of Quantum Chromodynamics (QCD).

hep-ph↗

arXiv2023

Yukawa theory in non-perturbative regimes: towards confinement, exact $\beta$-function and conformal phase

We study possible hints towards confinement in a Z$_2$-invariant Yukawa system with massless fermions and a real scalar field in the strongly-coupled regime. Using the tools developed for studying non-perturbative physics via Jacobi elliptical functions, for a given but not unique choice of the vacuum state, we find the exact Green's function for the scalar sector so that, after integrating out the scalar degrees of freedom, we are able to recover the low-energy limit of the theory that is a fully non-local Nambu-Jona-Lasinio (NJL) model. We provide an analytical result for the Renormalization Group (RG) running of the self-interaction coupling in the scalar sector and critical indexes in the strongly-coupled regime. In the fermion sector, we provide some clues towards confinement, after deriving the gap equation with the non-local NJL model, a property which is well-known to not emerge in the local limit of this model. We conclude that, for the scalar-Yukawa theory in the non-perturbative domain with our choice of the vacuum state, the fundamental fermions of the theory form bound states and cannot be observed as asymptotic states.

hep-th↗

arXiv2023

Flavor Violating Di- Higgs Coupling

Di-Higgs couplings to fermions of the form $h^{2}\overline{f}f$ are absent in the Standard Model, however, they are present in several physics Beyond Standard Model (BSM) extensions, including those with vector-like fermions. In Effective Field Theories (EFTs), such as the Standard Model Effective Field Theory (SMEFT) and the Higgs Effective Field Theory (HEFT), these couplings appear at dimension 6 and can in general, be flavour-violating (FV). In the present work, we employ a bottom-up approach to investigate the FV in the lepton and quarks sectors through the di-Higgs effective couplings. We assume that all FV arises from this type of couplings and assume that the Yukawa couplings $Y_{ij}$ are given by their SM values, i.e. $Y_{ij} = \sqrt{2}m_{i}\delta_{ij}/v$. In the lepton sector, we set upper limits on the Wilson coefficients $C_{ll'}$ from $l \rightarrow 3l'$ decays, $l \rightarrow l\gamma$ decays, muonium oscillations, the $(g-2)_{\mu}$ anomaly, LEP searches, muon conversion in nuclei, FV Higgs decays, and $Z$ decays. We also make projections on some of these coefficients from Belle II, the Mu2e experiment and the LHC's High Luminosity (HL) run. In the quark sector, we set upper limits on the Wilson coefficients $C_{qq'}$ from meson oscillations and from $B$-physics searches. A key takeaway from this study is that current and future experiments should set out to measure the effective di-Higgs couplings $C_{ff'}$, whether these couplings are FV or flavour-conserving. We also present a matching between our formalism and the SMEFT operators and show the bounds in both bases.

hep-ph↗

arXiv2023

Renormalisable Non-local Quark-Gluon Interaction: Mass Gap, Chiral Symmetry Breaking & Scale Invariance

We derive a Nambu--Jona-Lasinio (NJL) model from a non-local gauge theory and show that it has confining properties at low energies. In particular, we present an extended approach to non-local QCD and a complete revision of the technique of Bender, Milton and Savage applied to non-local theories, providing a set of Dyson--Schwinger equations in differential form. In the local case, we obtain closed form solutions in the simplest case of the scalar field and extend it to the Yang--Mills field. In general, for non-local theories, we use a perturbative technique and a Fourier series and show how higher-order harmonics are heavily damped due to the presence of the non-local factor. The spectrum of the theory is analysed for the non-local Yang--Mills sector and found to be in agreement with the local results on the lattice in the limit of the non-locality mass parameter running to infinity. In the non-local case, we confine ourselves to a non-locality mass that is sufficiently large compared to the mass scale arising from the integration of the Dyson--Schwinger equations. Such a choice results in good agreement, in the proper limit, with the spectrum of the local theory. We derive the gap equation for the fermions in the theory that gives some indication of quark confinement in the non-local NJL case as well. Confinement seems to be a rather ubiquitous effect that removes some degrees of freedom in the original action, favouring the appearance of new observable states, as seen, e.g.,\ for quantum chromodynamics at lower energies.

hep-ph↗

arXiv2022

A Critical Analysis of Classifier Selection in Learned Bloom Filters

Learned Bloom Filters, i.e., models induced from data via machine learning techniques and solving the approximate set membership problem, have recently been introduced with the aim of enhancing the performance of standard Bloom Filters, with special focus on space occupancy. Unlike in the classical case, the "complexity" of the data used to build the filter might heavily impact on its performance. Therefore, here we propose the first in-depth analysis, to the best of our knowledge, for the performance assessment of a given Learned Bloom Filter, in conjunction with a given classifier, on a dataset of a given classification complexity. Indeed, we propose a novel methodology, supported by software, for designing, analyzing and implementing Learned Bloom Filters in function of specific constraints on their multi-criteria nature (that is, constraints involving space efficiency, false positive rate, and reject time). Our experiments show that the proposed methodology and the supporting software are valid and useful: we find out that only two classifiers have desirable properties in relation to problems with different data complexity, and, interestingly, none of them has been considered so far in the literature. We also experimentally show that the Sandwiched variant of Learned Bloom filters is the most robust to data complexity and classifier performance variability, as well as those usually having smaller reject times. The software can be readily used to test new Learned Bloom Filter proposals, which can be compared with the best ones identified here.

cs.LG↗