arXiv subjects

Michele Caselle

Publications and source records attributed to Michele Caselle.

At least 19 recordsLinked to original sources

arXiv2026

Confining Flux Tube in the Trace Deformed (2+1) Dimensional SU(2) Gauge Theory

We study the confining flux tube in the reconfined phase of trace deformed SU(2) Yang-Mills theory in (2+1) dimensions. Using lattice simulations above the standard deconfinement temperature, we analyze Polyakov-loop correlators and extract the ground state energy of the effective string. We show that the usual Nambu-Goto effective string description, including its standard higher-order corrections, fails to reproduce the data as the trace deformation is increased. Remarkably, deep in the reconfined regime the results are instead accurately described by the Polchinski-Yang rigid-string solution, corresponding to an effective string dominated by an extrinsic-curvature term. We further investigate the transverse profile of the chromo-electric flux tube and find significant deviations from the standard Yang-Mills behavior, including a substantial modification of the intrinsic width. Finally, we present an exploratory study of the phase diagram, finding evidence for a transition from a continuous to a first order reconfinement line as the deformation parameter increases. These results suggest that the reconfined phase realizes a qualitatively different effective-string regime from ordinary confinement.

hep-lat↗

arXiv2026

Pulling strings in real time: flux tube dynamics in (2+1)-d $\mathbb{Z}_2$-Higgs Gauge Theories

Understanding real-time flux-tube dynamics in more than one spatial dimension is key to unlocking the non-perturbative physics of confinement, and is now actively pursued by quantum computing and simulation experiments. However, describing such dynamics has proven to be extremely challenging with both experiments and state-of-the-art numerical simulations limited to small volumes and short timescales. Here we investigate flux tube statics and real-time evolution in a genuine two-dimensional $\mathbb{Z}_2$ Higgs gauge theory at system sizes and timescales order of magnitude beyond present experiments and numerics. The key enabling element is the recently introduced Clifford-augmented matrix product states (CAMPS) framework, which we demonstrate to parametrically reduce the entanglement that must be represented in the matrix product state; both in the pure-gauge limit and in the presence of dynamical matter. We benchmark this capability through stringent tests of effective string theory, including universal spectral features and flux tube roughening properties in presence of matter. We then introduce a string-pull protocol that selectively excites transverse modes and reconstructs their finite-size spectrum in real time. In the rough regime, the response is collective, and our simulations show that this is also well captured by universal effective string theory predictions. Strong confinement instead produces long-lived, lattice-locked local dynamics persisting to times $tJ \gtrsim 100$. These results provide ab initio evidence that effective string theory captures nonequilibrium string dynamics and reveal a hitherto unexplored long-lived prethermal regime of strongly confined flux tubes, providing a novel angle on how confinement dictates dynamics in more than one spatial dimension.

quant-ph↗

arXiv2026

The Advantage of Fine-Grained Training

In classification problems, models are trained to predict a class label based on the input data features. However, class labels are organized hierarchically in many datasets. While a classification task is often defined at a specific level of this hierarchy, training can utilize a finer granularity of labels. Empirical evidence suggests that such fine-grained training can enhance performance. In this work, we investigate the generality of this observation and explore its underlying causes using both real and synthetic datasets. We show that training on fine-grained labels does not universally improve classification accuracy. Instead, the effectiveness of this strategy depends on the geometric structure of the data and its relations with the label hierarchy. Specifically, we show that the advantage of fine-grained training crucially depends on the degree of alignment between the decision boundaries required for the fine- and coarse-grained tasks, a property that we term boundary redundancy. Additionally, factors such as dataset size and model capacity significantly influence whether fine-grained labels provide a performance benefit. Indeed, we identify a transition, whose location is largely controlled by the degree of overparameterization, separating regimes where fine-grained training improves performance from those where direct coarse-grained training is preferable.

cs.LG↗

arXiv2026

Alternative routes to universal diversity scaling in component systems: from proteomes to large language models

Remarkably common statistical laws characterize the diversity scaling and its fluctuations across a wide range of complex "component systems". These regularities are often interpreted as signatures of an underlying innovation mechanism driving the growth of component diversity, but the basic ingredients necessary for their emergence remain poorly understood. In particular, from language and technological artifacts to genomes and gene expression patterns, the number of distinct components grows sublinearly with system size, while its variance scales approximately as the square of its mean. This behavior is consistent across diverse systems, raising the question of whether general constraints or emergent principles underlying diversity and innovation define the architectures of realizations with different numbers of components. To address this question, we derive analytical conditions for the joint emergence of these two diversity laws within a broad class of growth models, showing that they require a specific asymptotic dependence of the innovation probability on diversity and system size. We then demonstrate that the same macroscopic laws arise in a different class of models with latent heterogeneity, where quadratic fluctuation scaling always emerges asymptotically as a consequence of general statistical principles, essentially the law of total variance, without explicitly assuming an innovation mechanism or any specific rule for system assembly. We compare these predictions with empirical data from language, genomes, LEGO constructions, and texts generated by large language models. Our results show that empirical diversity scaling laws strongly constrain generative models but do not uniquely identify the mechanisms generating diversity, revealing a close correspondence between innovation-driven growth models and latent-variable descriptions.

cond-mat.stat-mech↗

arXiv2026

Intrinsic Width of the Flux Tube as a tool to explore confining mechanisms in Lattice Gauge Theories

We study the profile of the flux tube in the SU(2) gauge model in 2+1 dimensions, with a particular attention to the so called "intrinsic width" which drives the exponential decay of the flux density at large transverse distances. This quantity is directly related to the confining mechanism which generates the flux tube: to test the properties of the latter we study a wide range of different values of lattice spacing, temperature and flux tube lengths and show that our data are precise enough to distinguish between different confining models. In particular we show that at high temperatures (just below the deconfinement transition) the data are perfectly described by an Ising-like effective model based on the Svetitsky-Yaffe mapping. At lower temperatures this approximation does not hold anymore. In this regime (which is the most interesting one from a physical point of view) we test several alternative proposals and show that the dual superconductor model is the one which better fits the data. However, this proposal is not fully satisfactory, because the values of the Ginzburg-Landau parameter extracted from the fits increase with the length of the flux tube, which is not a feature predicted by the model. This suggests that a more sophisticated model is needed to explain confinement in non-abelian gauge theories and, at the same time, that our data on the intrinsic width may be a powerful tool to benchmark these candidates.

hep-lat↗

arXiv2026

Lattice Determination of the Baryon Junction Mass in $(2+1)$ Dimensions

This contribution investigates baryonic flux tube configurations in $SU(3)$ Yang--Mills theory in $(2+1)$ dimensions. Leveraging recent next-to-leading-order results within the Effective String Theory (EST) framework, which explicitly include corrections proportional to the baryon junction mass $M$ up to order $1/R^2$, we carry out a non-perturbative determination of this parameter, through high-precision simulations of the three-point Polyakov-loop in the open string channel. In addition, the high-temperature regime of the baryonic system is examined in order to test the Svetitsky--Yaffe conjecture. Close to the deconfinement transition, the lattice results for the correlators show close agreement with the predictions of the two-dimensional three-state Potts model.

hep-lat↗

arXiv2026

Intrinsic Width of the flux tube in 2+1 dimensional Yang-Mills theories

We present our updated results on the intrinsic width of the profile of the flux tube in (2+1)-dimensional Yang-Mills theory with SU(2) gauge group. We identify the intrinsic width as the characteristic length scale of the exponentially decaying tails of the profile of the flux tube. Inspecting a broad range of temperature, we check that this length does not depend on the length of the flux tube. Our estimations of the intrinsic width show a constant value at low temperature and a growing trend approaching the deconfinement temperature that can be understood from the universality class of the phase transition via the Svetitsky-Yaffe mapping.

hep-lat↗

arXiv2025

Casimir effect in critical $\mathrm{O}(N)$ models from non-equilibrium Monte Carlo simulations

$\mathrm{O}(N)$ vector models in three dimensions, when defined in a geometry with a compact direction and tuned to criticality, exhibit long-range fluctuations which induce a Casimir effect. The strength of the resulting interaction is encoded in the excess free-energy density, which depends on a universal coefficient: the Casimir amplitude. We present a high-precision numerical calculation of the latter, by means of a novel non-equilibrium Monte Carlo algorithm, and compare our findings with results obtained from large-$N$ expansions and from the conformal bootstrap.

cond-mat.stat-mech↗

arXiv2025

The Mass of the Baryon Junction: a lattice computation in 2 +1 dimensions

We present a systematic study of baryonic flux tubes in SU(3) Yang-Mills theory in (2+1) dimensions. A recent next-to-leading-order derivation within the Effective String Theory framework has, for the first time, made explicit the corrections proportional to the mass of the baryon junction M, up to order $1/R^2$ (where $R$ is the length of the confining strings), opening the possibility of its non-perturbative determination. One of the main goals of this paper is, through high precision simulations of the three-point Polyakov loop correlator, to measure for the first time the baryon junction mass. By isolating the predicted $1/R^2$ term in the open string channel, we obtain the value $M/\sqrtσ = 0.1355(36)$, similar to the phenomenological value which is used to describe hadrons, although our computation was done in (2+1) dimensions. In addition, studying the high temperature behavior of the baryon, we present a new test of the Svetitsky-Yaffe conjecture for the SU(3) theory in three dimensions. Focusing on the high temperature regime, just below the deconfinement transition, we compare our lattice results for Polyakov loop correlators with the quantitative predictions obtained by applying conformal perturbation theory to the three-state Potts model in two dimensions and find excellent agreement.

hep-lat↗

arXiv2025

Studying Effective String Theory using deep generative models

Effective String Theory (EST) offers a robust non-perturbative framework for describing confinement in Yang-Mills theory by treating the confining flux tube between a static quark-antiquark pair as a thin, vibrating string. While EST calculations are typically carried out using zeta-function regularization, certain problems-such as determining the flux tube width-are too complex to solve analytically. However, recent studies have demonstrated that EST can be explored numerically by employing deep learning techniques based on generative algorithms. In this work, we provide a brief introduction to EST and this novel numerical approach. Finally, we present results for the width of the Nambu-Gotö EST.

hep-lat↗

arXiv2025

Ranking nodes in bipartite systems with a non-linear iterative map

Ranking nodes in networks according to a defined measure of importance is an extensively studied task, with applications in ecology, economic trade networks, and social networks. This paper introduces a method based on a non-linear iterative map to evaluate node relevance in bipartite networks. By tuning a single parameter $γ$, the method captures different concepts of node importance, including established measures like degree centrality, eigenvector centrality and the fitness-complexity ranking. The algorithm's flexibility allows for efficient ranking optimization tailored to specific tasks, outperforming state-of-the-art algorithms. We apply this method to ecological mutualistic networks, where ranking quality can be assessed by the extinction area - the rate at which the system collapses when species are removed in a certain order. The map with the optimal $γ$ value surpasses existing ranking methods on this task. Additionally, our method excels in evaluating nestedness, another crucial structural property of ecological systems, requiring specific node rankings. Finally, we explore theoretical aspects of the map, revealing a phase transition at a critical $γ$ dependent on the data structure that can be characterized analytically for random networks. Near the critical point, the map exhibits unique features and a distinctive "triangular" packing pattern of the incidence matrix.

cond-mat.stat-mech↗

arXiv2025

On the equation of state of U(1) lattice gauge theory in three dimensions

We study the equation of state of three-dimensional compact U(1) gauge theory on the lattice by means of numerical simulations, and discuss the implications of our results for the spectrum of the theory, in connection with previous results from the literature. We also compare our findings to the case of non-Abelian gauge theories and comment on the continuum limit.

hep-lat↗

arXiv2025

Numerical determination of the width and shape of the effective string using Stochastic Normalizing Flows

Flow-based architectures have recently proved to be an efficient tool for numerical simulations of Effective String Theories regularized on the lattice that otherwise cannot be efficiently sampled by standard Monte Carlo methods. In this work we use Stochastic Normalizing Flows, a state-of-the-art deep learning architecture based on non-equilibrium Monte Carlo simulations, to study different effective string models. After testing the reliability of this approach through a comparison with exact results for the Nambu-Gotō model, we discuss results on observables that are challenging to study analytically, such as the width of the string and the shape of the flux density. Furthermore, we perform a novel numerical study of Effective String Theories with terms beyond the Nambu-Gotō action, including a broader discussion on their significance for lattice gauge theories. The combination of these findings enables a quantitative description of the fine details of the confinement mechanism in different lattice gauge theories. The results presented in this work establish the reliability and feasibility of flow-based samplers for Effective String Theories and pave the way for future applications on more complex models.

hep-lat↗

arXiv2025

Effective string description of the reconfined phase in the trace deformed $\mathrm{SU}(2)$ Yang-Mills theory in (2+1) dimensions

We study the behaviour of the flux tube in the reconfined phase of the trace deformed $\mathrm{SU}(2)$ Yang-Mills theory in (2 + 1) dimensions. In this phase the Polyakov loop has a vanishing expectation value (and center symmetry is recovered) even at high temperatures. We study, by means of numerical simulations, the confining potential between two Polyakov loops. We show that its behaviour is very different from that of usual confining gauge models and shows a remarkable agreement with the predictions of the so called "rigid string" in the limit in which the rigidity term (i.e. a term proportional to the square of the extrinsic curvature of the string) is very large and is the dominant contribution in the action.

hep-lat↗

arXiv2025

Stochastic normalizing flows for Effective String Theory

Effective String Theory (EST) is a powerful tool used to study confinement in pure gauge theories by modeling the confining flux tube connecting a static quark-anti-quark pair as a thin vibrating string. Recently, flow-based samplers have been applied as an efficient numerical method to study EST regularized on the lattice, opening the route to study observables previously inaccessible to standard analytical methods. Flow-based samplers are a class of algorithms based on Normalizing Flows (NFs), deep generative models recently proposed as a promising alternative to traditional Markov Chain Monte Carlo methods in lattice field theory calculations. By combining NF layers with out-of-equilibrium stochastic updates, we obtain Stochastic Normalizing Flows (SNFs), a scalable class of machine learning algorithms that can be explained in terms of stochastic thermodynamics. In this contribution, we outline EST and SNFs, and report some numerical results for the shape of the flux tube.

hep-lat↗

arXiv2025

Intrinsic width of the flux tube in 2+1 dimensional Yang-Mills therories

We study the shape of the flux tube in lattice Yang-Mills theories and in particular its intrinsic width. In the framework of the Effective String Theory description of the confining flux tube this intrinsic width has no measurable effects on the inter-quark static potential, but it can be precisely detected looking at the profile of the flux tube. We address this problem with a set of high precision simulations in the (2+1) dimensional SU(2) model. We find two different behaviours as a function of the temperature. In the low temperature regime ($T \ll T_c$) we find a good agreement with an expression inspired by the dual superconductive model of confinement. In the high temperature regime ($T \lesssim T_c$) our data agree with a model based on the Svetitsky-Yaffe mapping. All our data in this regime can be described in terms of only one length scale, the intrinsic width, which turns out to be the same scale appearing in the confining inter-quark static potential.

hep-lat↗

arXiv2024

Effective String Theory of three-dimensional SU(N) gauge theories beyond the Nambu--Gotō approximation

We study the effective bosonic string that describes confining flux tubes in three-dimensional SU(N) Yang--Mills theories. Although the low-energy properties are universal and well described by the Nambu--Gotō action, the subtle dependence on the gauge group is embedded in a series of corrections, which remain undetermined, appearing in the expansion around the limit of an infinitely long string. We extract the first two of these corrections from a set of high-precision Monte Carlo simulations of Polyakov loop correlators at finite temperatures close to the deconfinement transition. We present and compare the results of new lattice simulations for theories with N=3 and N=6 color charges, along with an improved estimate for the N=2 case, discussing the approach to the large-N limit. We show that our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. Additionally, we present a new test of the Svetitsky--Yaffe conjecture for the SU(3) theory in three dimensions, showing that our results for the correlator of Polyakov loops perfectly agree with the predictions obtained using a conformal perturbation approach to the two-dimensional three-state Potts model

hep-lat↗

arXiv2024

Microsecond-Latency Feedback at a Particle Accelerator by Online Reinforcement Learning on Hardware

The commissioning and operation of future large-scale scientific experiments will challenge current tuning and control methods. Reinforcement learning (RL) algorithms are a promising solution thanks to their capability of autonomously tackling a control problem based on a task parameterized by a reward function. The conventionally utilized machine learning (ML) libraries are not intended for microsecond latency applications, as they mostly optimize for throughput performance. On the other hand, most of the programmable logic implementations are meant for computation acceleration, not being intended to work in a real-time environment. To overcome these limitations of current implementations, RL needs to be deployed on-the-edge, i.e. on to the device gathering the training data. In this paper we present the design and deployment of an experience accumulator system in a particle accelerator. In this system deep-RL algorithms run using hardware acceleration and act within a few microseconds, enabling the use of RL for control of ultra-fast phenomena. The training is performed offline to reduce the number of operations carried out on the acceleration hardware. The proposed architecture was tested in real experimental conditions at the Karlsruhe research accelerator (KARA), serving also as a synchrotron light source, where the system was used to control induced horizontal betatron oscillations in real-time. The results showed a performance comparable to the commercial feedback system available at the accelerator, proving the viability and potential of this approach. Due to the self-learning and reconfiguration capability of this implementation, its seamless application to other control problems is possible. Applications range from particle accelerators to large-scale research and industrial facilities.

physics.acc-ph↗