Numerical Study About The Sub-leading Term Of The Strong Coupling Expansion Of The Heavy-Quark Potential In A N=4 Super Yang-Mills Vacuum

Heavy-quark potential is a quantity of importance,which probes the confinement mechanism in the hadronic phase and meson melting in the plasma phase.One could assess the robustness of the leading order prediction by exploring the sub-leading order correction.The purpose of this paper is to evaluate the sub-leading term of strong coupling expansion of heavy-quark potential in N=4 SYM vacuum.According to AdS/CFT correspondence,the strong coupling expansion of N=4 SYM corresponds to the semi-classical expansion of string-sigma model in AdS₅×S⁵.Many important quantities in N=4 SYM could be read out from the Wilson loop expectation value,while one of these quantities is the heavy-quark potential which can be extracted from the straight line Wilson loop and parallel lines Wilson loop.The expectation value of Wilson loop corresponds to the path integral of world sheet action in string-sigma model.The string-sigma action in classical limit namely the classical action corresponds to the leading term of Wilson loop expectation value.By expanding the string-sigma action to the quadratic order of the fluctuating coordinates around the classical limit and carrying out the path integral,one can get one loop partition function,and then the one loop effective action,finally get the one loop correction namely the sub-leading term of the Wilson loop expectation value.The one loop effective actions have already been obtained for the straight line and parallel lines,they are expressed in terms of functional determinants acting on fluctuating coordinates.This paper based on these one-loop effective actions obtained,reduced evaluating functional determinants to a set of second order ordinary differential equations, then considered the singularities of the differential equations which could not resolved analytically.Finally,we got significant numerical results.