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Principle Investigator: Kim Splittorff (NBI) The Sapere Aude Program of The Danish Council for Independent Research Background: A major unsolved problem in physics is to understand the non-perturbative regime of quark matter. At high temperature and density perturbation theory predicts that a sea of quarks and gluons will be formed. The properties of this sea of quarks and gluons is, however, strikingly different from the state of matter in our present universe where the quarks and gluons are confined into hadrons such as protons and pions. A transition occurs at which the particles that constitute the matter of our Universe today are formed. The study of this central transition from first principles is a major challenge because the tools for the required non-perturbative treatment of the strong interactions are lacking. The central aim of this project is to develop and explore the necessary first principle non-perturbative tools. The Sign Problem: Monte Carlo simulations, the key non-perturbative tool for the study of the gauge theory of strong interactions (QCD), may only be used when the net density of baryons is zero. As soon as an imbalance between the number of quarks and antiquarks is introduced the Monte Carlo approach (lattice QCD) breaks down. The problem with the Monte Carlo approach arises because the action for a quantum system in Euclidean space is not necessarily real. When the Euclidean action assumes complex values the theory is said to have a sign problem. In the theory of the strong interactions such a sign problem is present at any nonzero value of the baryon density. To induce a net quark number density one introduces a chemical potential which favors quarks over antiquarks and this quark chemical potential makes the quark determinant and hence the action complex. Physically there is nothing wrong with having a complex action; on the contrary, it is a direct consequence of the imbalance one seeks to induce between particles and antiparticles. For this reason sign problems are a general phenomenon which are encountered frequently also in solid state physics. The problem with systems where the Euclidean action assumes complex values is that the measure in the path integral which defines the partition function is not a probability measure. Numerical Monte Carlo methods which compute the partition function using a probabilistic evaluation of gauge field configurations are therefore problematic. In QCD at nonzero quark chemical potential the strength of the sign problem for standard Monte Carlo methods grows exponentially with the volume and thus hinders a numerical evaluation of the thermodynamical limit. The Project: To understand the nature of phase transitions in dense strongly interacting matter directly from the underlying microscopic theory, we will develop and explore new first-principle non-perturbative tools. The results of these first principle non-perturbative computations at non-zero baryon density will provide a key benchmark in the quest for the phase diagram of strongly interacting matter. |
split@nbi.dk, (+45) 353 25359, (+45) 2489 2498