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Random matrix theory and quantum chromodynamics


Research objectives and content
The mechanism of quark confinement is a long-standing puzzle in the theory of strong interactions (Quantum Chrornodynamics or QCD). At the QCD phase transition, chiral symmetry is restored and the quarks unbind to form a quark-gluon plasma. It has recently become clear that the powerful techniques of random matrir theory can be utilized for obtaining analytical information on this phase transition. In contrast, nulllerical lattice simulatiolls can at most guide us in the search for a theoretical understanding of confinement, and perturbation theory can not provide any information on such strong coupling phenomena. The applicant has with her research group proved a universality conjecture, that justifies the choice an arbitrary matrix model potential, so that the random matrix theory used to study QCD or another gauge theory is solvable. In a recent preprint (hep-th/9712006) we have extended this analysis to multicritical matrix models, which represent the symmetry restoration (deconfinement) scenario in QCD. The goal of this project is 1) to study the multicritical scenario further, proving, if possible, universality at any arbitrary muticritical point, 2) to obtain analytical informa- tion concerning the QCD phase transition using random matrix theory, 3) to clarify the connection between random matrix theory and gauge theories. and 4) to obtain informa- tion on the fundamental mechanislll of quark confinement. The objective of this proposal coincides with two of the main goals of the Community Physics Network 'Quantum as- pects of gauge theories, supersymmetry and unification' (points 1) and 3) in the Work Programme). which the University of Torino is part of.
Training content (objective, benefit and expected impact)
Both the applicant and the host research group is expected to benefit from a collab- o ration. The proposal constitutes a natural extension of their previous work. Also, it would contribute new results to a timely issue Ol1 the forefront of modern physics, within a European framework. and hopefully lead to substantial progress on one of its fundamental puzzles. Links with industry / industrial relevance (22)
The proposed project represents fundamental research and has no foreseen d*ect industrial applications.

Funding Scheme

RGI - Research grants (individual fellowships)
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Istituto Nazionale di Fisica Nucleare
Via P.giuria
10125 Torino