PACIFIC QUANTUM CENTER
RFBR Grant: 18-02-40130 мега
Abstract:
One of the main tasks of theoretical physics in the field of strong interactions of elementary particles is the study of QCD with a nonzero baryon chemical potential. The importance of this task is determined by the need to know the properties of QCD with a nonzero baryon density to understand the results of heavy-ion collisions experiments, as well as the properties of compact stars.
Lattice QCD is one of the few theoretical approaches that allows the study of the nonperturbative properties of QCD based on the first principles of quantum field theory. Important results (transition temperature, equation of state) were obtained in lattice QCD with zero baryon chemical potential and nonzero temperature. However, with a nonzero baryon chemical potential, standard computational methods of lattice QCD do not work. There are ways to get fairly reliable results for small values of baryon chemical potential, for example, calculating the coefficients of the Taylor series. However, there are no computational methods for large values of the baryon chemical potential. In this situation, a number of authors have proposed the study of theories, which in their properties may be close to the properties of QCD for large values of the baryon chemical potential. In this project we will study one of such theories - QCD with the gauge group SU (2), or SU (2) QCD.
SU (2) QCD is the simplest non-Abelian gauge theory without the sign problem for a finite quark density. This project is aimed at studying the properties and calculating a large number of physical observables in this theory at nonzero temperature and high quark density, as well as developing and testing new computational methods applicable in the usual 3-color lattice QCD for large values of baryon chemical potential. The results will also allow us to create a testing ground for testing other nonperturbative approaches at finite density, which include additional simplifications or assumptions.
It is planned to study such phenomena as the confinement-deconfinement transition in the phase plane, temperature-quark chemical potential, properties of the color-magnetic sector of the theory for large values of the quark chemical potential. We also plan to study the equation of state, the mechanism of mass gap formation in the fermion spectrum, the properties of gluons in a dense medium, the influence of a dense medium on the topological properties of QCD, the possibility of the existence of the quarkionic phase in this theory, fluctuations of quark density.
The results obtained in this project will make predictions for QCD with high baryon density and low temperature — an area of the phase diagram that is critical for future experiments at the NICA accelerator complex. In addition, the results of the presented project will be important in various applications to the physics of neutron stars.
Аннотация
Одной из главных задач теоретической физики в области сильных взаимодействий элементарных частиц является изучение КХД при ненулевом барионном химическом потенциале. Важность этой задачи определяется необходимостью знания свойств КХД при ненулевой барионной плотности для понимания результатов экспериментов по столкновениям тяжелых ионов, а также свойств компактных звезд.
Решеточная КХД является одним из немногих теоретических подходов, который позволяет исследование непертурбативных свойств КХД, исходя из первых принципов квантовой теории поля. Важные результаты (температура перехода, уравнение состояния) были получены в решеточной КХД при нулевом барионном химическом потенциале и ненулевой температуре. Однако, при ненулевом барионном химическом потенциале стандартные методы вычислений в решеточной КХД не работают. Есть способы получить довольно надежные результаты при небольших значениях барионного химического потенциала, например, вычисление коэффициентов ряда Тейлора. Однако методов вычислений для больших значений барионного химического потенциала пока нет. В этой ситуации рядом авторов было предложено изучение теорий, которые по своим свойствам могут быть близки к свойствам КХД при больших значениях барионного химического потенциала. В данном проекте мы будем изучать одну из таких теорий - КХД с калибровочной группой SU(2), или SU(2) КХД.
SU(2) КХД, является простейшей неабелевой калибровочной теорией без проблемы знака при конечной плотности кварков. Данный проект направлен на изучение свойств и вычисление большого числа физических наблюдаемых в этой теории при ненулевой температуре и большой кварковой плотности, а также на разработку и проверку новых методов вычислений, применимых в обычной 3-х цветной решеточной КХД при больших значениях барионного химического потенциала. Полученные результаты также позволят создать полигон для проверки других непертурбативных подходов при конечной плотности, которые включают дополнительные упрощения или допущения.
Планируется изучить такие явления как переход конфайнмент - деконфайнмент в фазовой плоскости температура - кварковый химический потенциал, свойства цвето-магнитного сектора теории при больших значениях кваркового химпотенциала. Мы также планируем изучить уравнение состояния, механизм образования массовой щели в фермионном спектре, свойства глюонов в плотной среде, влияние плотной среды на топологические свойства КХД, возможность существования кваркионной фазы в этой теории, флуктуации кварковой плотности.
Результаты, полученные в данном проекте, позволят сделать предсказания для КХД с большой барионной плотностью и низкой температурой - областью фазовой диаграммы, критически важной для будущих экспериментов на ускорительном комплексе NICA. Помимо этого, результаты представленного проекта, будут важны в различных приложениях к физике нейтронных звезд.
RFBR Grant: 18-02-40121 мега
Abstract:
Understanding the properties of quark-gluon plasma is one of the most difficult tasks of modern high-energy physics. Due to the so-called "sign problem", the physical characteristics of a dense plasma cannot be studied even with the most modern numerical methods. Usually, the sign problem is bypassed using an imaginary baryon chemical potential with the subsequent analytic continuation into a region of real chemical potentials. This method, applicable to low-density plasma, is not entirely suitable for the dense plasma, which will be created in the NICA facility in Dubna. Our goal is to use the latest information processing methods for the numerical study of the finite-temperature properties of QCD plasma at a high baryon chemical potential, corresponding to the conditions created in central and off-center collisions of heavy ions in NICA. We will use standard Monte-Carlo numerical simulation enhanced by machine learning methods such as Deep Neural Networks enhanced by Supervised Learning, and Generative Adversarial Networks in conjunction with Variational Autoencoders. We plan to simulate lattice QCD with two flavors of “improved” Wilson quarks with imaginary chemical potential and then conduct an analytical continuation into the real chemical potential using the machine learning methods. The learning algorithm will first be trained on simpler gauge models in which the sign problem is either solved or does not exist at all (we will use models of the Ising type, two-color QCD and QCD with finite isospin density). The algorithm will then be applied to the QCD data generated by improved Monte-Carlo techniques at an imaginary chemical potential. Using this strategy, we plan to study the QCD phase diagram and its thermodynamic properties with nonzero density and high temperature, which are currently unavailable for either analytical or numerical approaches.
The first stage of the project was devoted to the development of tools for analysis by machine learning of field lattice configurations of the gauge theory with the symmetry group SU (2) and SU (3), as well as scalar field theory. Also, at the first stage, the applicability of neural network approaches to QCD configurations was tested at zero chemical potential (in the absence of baryon density). The studies show that a neural network using lattice configurations as input and trained for two values of the lattice coupling constant can accurately predict the dependence of the observed theory on the lattice coupling constant in the entire range. A neural network operating directly with field configurations could isolate the essential observables that reflect the properties of the theory under study. For example, when studying the critical behavior of a theory, a neural network identifies combinations of field variables that correspond to an order parameter (Polyakov lines). Also, at the first stage of the project, machine learning methods were used to study the properties of field theory on a lattice with nontrivial topology. After the training phase, the neural network can quickly predict the Casimir energy of arbitrary finite regions with Dirichlet boundaries.
The second stage of the project was devoted to applying the methods developed at the first stage to the study of the phase structure of the gauge theory SU (3) and QCD at a finite density. We also carried out studies on topological objects (particularly magnetic monopoles) in a simplified model of confinement - the compact theory U (1) and real configurations of a gluon field at finite baryon densities. We found that a neural network trained in calibration field configurations with nonphysical lattice parameter values as input creates a gauge-invariant function and finds correlations with a valid target observable in the physical domain of the parameter space. Thus, for the first time, we developed a numerical analog of the analytic continuation from easily accessible but physically uninteresting regions of the parameter space to interesting but potentially inaccessible areas. Using the example of the compact gauge theory U (1) in three dimensions of space-time, we developed a neural network that analyzes magnetic monopoles' configurations and predicts the deconfinement transition point and several observables. We show that the developed neural network trained with configurations of one lattice size can predict the behavior of observables for other lattice sizes.