String Theory seminar - Masanori Hanada Seminar

Abstract: We give a microscopic mechanism of confinement in gauge theories including pure Yang-Mills and QCD, elaborating on "Confinement = BEC" mechanism proposed by Shimada, Wintergerst and MH. As a byproduct, we show a nontrivial behavior of Polyakov lines in the low-temperature regime of confining gauge theories: Polyakov lines are slowly varying Haar random modulo corrections exponentially small with respect to the inverse temperature. With exact Haar randomness, computation of two-point correlator of Polyakov loops reduces to the problem of random walk on group manifold. We show that linear confinement potential with approximate Casimir scaling of string tension follows naturally from such a random walk except for short distance. With exponentially small corrections to Haar randomness, string breaking and loss of Casimir scaling at long distance follow. Therefore, we obtain a Casimir scaling which is only approximate and valid only at intermediate distance --- This is precisely what we need to explain the results of lattice simulations! If time permits, I explain some other results on finite-N theories, too. This talk is based on my recent paper with Hiromasa Watanabe (arXiv:2310.07533, "On thermal transition in QCD") and a paper in preparation with Georg Bergner and Vaibhav Gautam.