NPQCD
Non-perturbative Quantum Chromodynamics
Scientific activities of the various Research Units
The main purpose of our research program is to investigate the nonperturbative (NP) sector of quantum chromodynamics (QCD) and related theories using state-of-the-art numerical and analytic methods.
As is well known QCD, the gauge theory describing strong interactions among quarks and gluons, is characterized by a strongly coupled, low-energy regime where standard perturbative tools fail. The study of the NP sector of QCD is of paramount importance for the understanding of the phase diagram at high temperature and density and its deep phenomenological implications related to the physics of heavy-ion collisions, the early Universe and the astrophysics of objects like compact stars.
The analysis of the large-distance NP sector of QCD can be successfully addressed by means of lattice gauge theory methods. This numerical approach, based on Wilson’s proposal, has its roots in the renormalization group theory and has been of inspiration for other approaches, like the one to Quantum Gravity based on dynamical triangulations.
There are still many open issues related to large-distance dynamics of QCD. Among them, the problem of understanding the mechanism of color confinement. Nobody doubts that the well-established phenomenon of confinement of quarks and gluons inside hadrons is encoded into the QCD Lagrangian. Yet, our current understanding does not go beyond that provided by a number of models of the QCD vacuum. In particular, a theoretical a priori explanation of the so-called area law in large size Wilson loops, which is closely related to a linear confining potential between a static quark and antiquark at large mutual distances, is still missing. In such a challenging situation, first-principle Monte Carlo simulations of QCD on a space-time lattice represent an indispensable tool not only for checking (or ruling out) models of confinement, but also for providing new numerical “phenomenology” and possibly stimulating original insights into the mechanism of confinement. Our planned studies on the flux tube dynamics in full QCD both at zero and finite T and/or in the presence of external background fields could shed light on the mechanism of confinement.
On the same ground it is important to get insight into the “theta dependence” of the theory. A reliable determination of the topological properties of full QCD at high T is essential to make a closer connection to the axion phenomenology in the early Universe. A precise knowledge of theta-dependence in SU(N) pure gauge theories and of its connection to other properties is important to better understand the NP structure of the theory. The question of the theta dependence and its relationship with chiral symmetries will also be investigated by means of Chiral Effective Lagrangians. At an algorithmic level, different methods to defeat the topological critical slowing down or for the reconstruction of the theta dependence will be tested on simple lattice models, including CP(N-1) and the 2D Heisenberg model, and extended to QCD.
In the last years, lattice simulations have contributed considerably to the understanding of QCD in extreme conditions. In particular, they have provided evidence about the presence of a finite T transition to a deconfined phase matter (as first predicted by N. Cabibbo and G. Parisi in 1975) accompanied by a restoration of chiral symmetry. Essential open questions regard what the intimate connection between deconfinement and chiral symmetry restoration is and how the location and the nature of the transition change as a function of external parameters of phenomenological or theoretical relevance. Unfortunately, lattice QCD simulations are hindered in some cases by the presence of complex factors in the functional integration measure (sign problem), theoretical progress in those cases relies on the application of presently known approximate methods to avoid the problem, or on possible future breakthroughs. A real breakthrough to overcome the infamous sign problem could come from exploiting quantum algorithms to evaluate thermal averages.
Another promising approach to the sign problem is based on dual representations of lattice gauge theories. This approach has been conveniently applied to spin models in the last decade to solve, fully or partially, the sign problem appearing in presence of nonzero chemical potentials and/or nontrivial topological terms, like the theta-term. The general strategy is to obtain dual representations with a positive Boltzmann weight starting from an effective model of Polyakov loops and integrating over them.
The mechanism of color confinement. [Bari, Cosenza]
Numerical simulations have established that there is a linear confining potential between a static quark and antiquark for distances equal to or larger than about 0.5 fm. This linear regime extends to infinite distances in SU(3) pure gauge theory, and, in the presence of dynamical quarks to distances of about 1.4 fm, where string breaking should take place. The long-distance linear quark-antiquark potential is naturally associated with a tube-like structure (“flux tube”) of the chromoelectric field in the longitudinal direction, i.e. along the line connecting the static quark and antiquark. In recent works we have obtained a comprehensive numerical description of the color field around static sources in pure SU3) gauge theory, via the measurement of all components of both chromoelectric and chromomagnetic fields on all transverse planes passing through the line between the quarks. We plan to extend our analysis to (2+1)-flavor QCD with physical quark masses, and to the finite temperature theory across the deconfinement transition.
Study of trace deformed SU(N) Yang-Mills theories. [Pisa]
Our previous studies (1807.06558, 1912.02662) have shown a clear connection between the realization of center symmetry restoration and the topological properties for trace deformed SU(N) gauge theories with a compactified direction, which also provide evidence for the expected volume independence of the theory in the large-N limit. We plan to extend the study to other non-perturbative quantities, including glueball and torelon masses. At the same time, we will study the properties of thermal monopoles and the behavior of the Dirac spectrum across the center restoring transition of the deformed theory, in order to make clearer the connection with color confinement and chiral symmetry breaking.
Theta-dependence and topological properties of strong interactions. [Pisa]
The main present issue regards the topological properties of full QCD, where a precise knowledge about theta-dependence, in particular regarding the behavior of the topological susceptibility as a function of temperature, can give useful constraints on axion cosmology and phenomenology. This can be partially approached by means of "Chiral Effective Lagrangians" with the inclusion of the theta term or the axion field. However, at T well above the chiral transition, one needs to focus on a program of development of new algorithmic and numerical strategies to overcome hard problems
related to the sampling of topological modes and to strong lattice artifacts. Apart from the multicanonical algorithm that we have introduced in 1807.07954, we will explore the introduction of spectral projector methods, in particular using the extension to staggered fermions that we have developed in 1908.11832.
Also, in the context of QCD-like theories, we plan to extend to SU(N) gauge theories the algorithm proposed by M.Hasenbusch in 1706.04443, in order to obtain a better characterization of the large N behavior and possibly extend the study of theta- dependence to other quantities of physical interest.
To deal with the sign problem in theories with a topological theta term, we will explore also analytical approaches based on dual variables, leading either to a positive Boltzmann weight or to a mitigation of the problem.
Phase diagram of QCD and universality. [Pisa]
We plan to perform a detailed study of some possible U(1) axial condensates in the high- temperature chirally-restored phase of QCD, both by means of nonperturbative analytical techniques, by expressing the functional averages in terms of the spectral density of the Euclidean Dirac operator and through an approximate evaluation of the path integral in the so-called "dilute instanton gas approximation", and by means of Monte Carlo simulations on the lattice.
At the same time, we plan to continue our numerical study regarding the prediction, based on universality arguments, for a first order transition in the chiral limit of QCD with a number of flavors N_F > 2. We have considered the issue recently (1702.00330) and results seem to contradict such predictions as the continuum limit is approached, thus challenging the validity of universality arguments: that claims for further studies with improved actions that we plan to pursue during the project. [Pisa]
QCD at finite chemical potential. [Bari, Cosenza, Ferrara, Pisa]
In the recent past we have made significant contributions pioneering and adopting the strategy of analytic continuation from imaginary chemical potential, this technique is now a standard which has produced solid results for many issues. Our plans for the present project are aimed at a better characterization of the physical properties around the RW transition, which is the only genuine transition that can be found in QCD for generic values of the quark masses. Various issues connected to the realization of chiral symmetry and to the confinement/deconfinement mechanism will be investigated: nature of the chiral transition, properties of the Dirac spectrum and study of the so-called mobility edge, properties of thermal monopoles.
At the same time, we plan to extend our study on the dependence of the electrical conductivity on magnetic field to the case of finite density, by means of analytic continuation techniques.
We also plan to develop a strategy to obtain dual representation with a positive Boltzmann weight. We plan to extend the approach to SU(N) and U(N) LGTs with full Wilson action, calculating corrections to the dual Boltzmann weight arising from the nonstatic part of the fermion determinant. We also plan to study the long-distance properties of gauge models at finite temperature and baryon density, with particular emphasis on the correlation function of Polyakov loops, the second-moment correlation length and the corresponding screening masses. Finally, we plan to investigate the liquid-like phase in a finite-density QCD. Since it is impossible at the moment to attack this problem in full QCD, we intend to investigate numerically those QCD regions where the dual weights are positive and numerical simulations can be performed. One such region is the high-density QCD where the leading contribution comes from the static fermion determinant.
Quantum Computing approaches to LGTs. [Bari, Ferrara, Pisa]
Present times are witnessing an increasing amount of interest towards the development of Quantum Computing approaches, especially in the Lattice Gauge Theory community.
Quantum Computing has the potential to provide answers to still unsolved problems, e.g., strongly interacting matter at finite baryon density or real-time dynamics. Our main interest at the moment is to understand how that will be realized in practice, once adequate Quantum Computing resources will be available; our focus is on the study of the QCD phase diagram, which requires the evaluation of thermal averages. That poses a number of conceptual and theoretical problems that need to be well understood in order to be prepared for the practical advent of Quantum Computing in the next years or decades: this is the main motivation and guideline of our research program in this field. After first results obtained in evaluating thermal averages in the case of a simple spin model which exhibits the sign problem (2001.05328), our aim is to extend the study to more complex, possibly gauge invariant, models. We also plan to fully investigate the implementation of quantum algorithms in the case of abelian and non-abelian LGTs, where issues related to gauge invariance arise. In particular, we will investigate prototype gauge theories with discrete gauge groups which, while requiring a limited number of qubits, still permit the testing of fundamental issues related to gauge invariance. We will study the complexity of the algorithms with respect to the computational depth and the systematic errors.
QCD under the influence of external background fields. [Pisa, Bari]
Our recent studies on the properties of QCD in strong magnetic background fields have left a few issues open which deserve further investigation. First of all, recently we have provided evidence for an anisotropic behavior of the electrical conductivity in the Quark- Gluon Plasma in the presence of a magnetic background field, with the conductivity enhanced in the direction of the magnetic field (1910.08516): that would be a direct evidence of the Chiral Magnetic Effect. It is therefore of utmost importance to put these studies on a more solid basis, by checking further various effects related to the finite lattice spacing and to the method used to extract the conductivity.
In addition to that, evidence for an anisotropic modification of the static quark-antiquark potential (1607.08160, 1807.01673) claims for further studies which could check whether a critical magnetic field at which the confining flux tube disappears and the string breaks, even at zero temperature. Such studies will require to go to very small lattice spacings, in order to ensure that a large magnetic field, up to 10Gev^2, can be introduced with negligible lattice artifacts.
Causal Dynamical Triangulations and NP renormalization of Quantum Gravity. [Pisa]
We will investigate the approach to Quantum Gravity based on Causal Dynamical Triangulations, aiming at exploiting some of the theoretical tools developed within the framework of Lattice QCD simulations. In particular, we plan to: i) make use of spectral methods to better understand and classify the geometries of triangulations sampled in CDT simulations; ii) explore the effect on the CDT phase diagram of the introduction of new operators in the CDT discretization; iii) explore the coupling of the pure gravity action to Abelian and non-Abelian gauge degrees of freedom. [Pisa]
Algorithmic improvements and computer optimization of LGT code. [Ferrara, Pisa, Bari]
We plan to investigate further algorithmic improvements to the computer codes routinely used by the collaboration, mainly in the area of exploring the algorithmic stability vs. the numerical efficiency of reduced precision arithmetics, as these computational techniques are becoming more and more used in modern computer architecture. We also plan to investigate the best scheduling of the compute intense part of the codes, in order to overlap computation with node-to-node communication, in order to have a better scaling behavior on massively parallel computers. [Ferrara, Pisa, Bari]
Map of INFN facilities
Next meeting
Login Form
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |