The Sub-leading Terms Of The Heavy-quark Potential And The Jet Quenching Parameter In Strongly Coupled N=4SYM Plasma

One of the main purposes of the heavy-ion collision experiments is to explore the QCD phase diagram and the properties of new state of matter created through heavy-ion collisions at high energy density. The experimental program at the Relativistic Heavy Ion Collider (RHIC) in Brookhaven National Laboratory provided strong evidences that new state of matter——QGP was created in the deconfinement phase of QCD and strongly coupled and it is also the matter that formed in the earlier universe in few microseconds after the big bang. Therefor, the research on QGP can help human being to explore the microscopic world and the origin of the universe. Usually QGP is generated in a very short time and can not be observed directly. So we need some probes and signals. The J/ψ suppression and the jet quenching are such two kinds of important hard probes.The heavy-quark potential and the jet quenching parameter discussed in this paper are such two concrete hard probes. The former can probe the confinement mechanism in the hadronic phase and meson melting in the plasma phase while the later can measure the energy loss of the jet which moves through the medium. And these two quantities can reveal some properties of the QGP. For a strongly coupled QGP suggested by RHIC data, perturbation method is not suitable and some non-perturbation approaches are desired. Usually the conventional non-perturbation methods are the Lattice QCD and the Schwinger-Dyson equation. The Lattice QCD can not deal with the real-time dynamics while the Schwinger-Dyson equation is very difficult to be solved. Therefor, they both have their own limitations.Nowadays, the another novel method can deal with the strongly coupled physics is the AdS/CFT correspondence. A prominent implication of the AdS/CFT duality is the correspon-dence between the superstring theory formulated on AdSs×S5and N=4supersymmetric Yang-Mills theory (SYM) in four dimensions. And according to the "strong-weak" correspon-dence of AdS/CFT, the strong coupling of the N=4can correspond to the weak coupling of the superstring theory. Because the leading orders of the heavy-quark potential and the jet quench-ing parameter in strongly coupled N=4SYM plasma computed by AdS/CFT correspondence are strictly valid only when the’t Hooft coupling constant goes to infinity and large Nc limit. However, with a finite value of A and the Nc=3, an understanding of how these computations are affected by finite λ corrections may be essential for more precise theoretical predictions. Meanwhile, by exploring these sub-leading orders correction, we could assess the reliability and robustness of the corresponding leading orders. Our aim is to evaluate the sub-leading terms of the heavy-quark potential and the jet quenching parameter in strongly coupled N=4SYM plasma.According to AdS/CFT correspondence, the strong coupling expansion of N=4SYM corre-sponds to the semi-classical expansion of the string-sigma model in AdSs×S5. Many important quantities, for example, heavy-quark potential and jet quenching parameter could be extracted from the expectation value of a Wilson loop. And the Wilson loop expectation value refers to the path integral of world sheet action in string-sigma model. Therefor, by calculating the string-sigma action in classical limit we can obtain the leading term of the Wilson loop expectation value; If we expand the string-sigma action to the quadratic order of the fluctuating coordinates around the classical limit and carrying out its path integral, we can obtain the one loop partition function and then the one loop effective action, at last we can obtain the one loop correction or in another word the sub-leading term of the Wilson loop expectation value. For the concrete calculation, the one loop effective actions are expressed in terms of functional determinants act-ing on fluctuating coordinates, then the calculation is reduced to evaluating functional determi-nants ratio to a set of second order ordinary differential equations. By applying the fourth-order Runge-Kutta method and Gelfand-Yaglom method to calculate these differential equations, we finally get the significant numerical results——the important contribution of the order O(λ-1/2).The paper is organized as follows. Chapter2subjects to the basis theory of QCD and AdS/CFT. We will present the calculation of the leading term and sub-leading term of the heavy-quark potential in N=4SYM vacuum and N=4SYM plasma in chapter3. Chapter4is about the calculation of the jet quenching parameter. Chapter5concludes the paper along with some discussions of the result and some open issues. Some calculation technique details are presented in the appendixes.