Regular Seminar Masanori Hanada (University of Surrey)
We propose a unified description of two important phenomena: color confinement in large-N gauge theory, and Bose-Einstein condensation (BEC). We focus on the confinement/deconfinement transition characterized by the increase of the entropy from N^0 to N^2, which persists in the weak coupling region. Indistinguishability associated with the symmetry group --- SU(N) or O(N) in gauge theory, and S_N permutations in the system of identical bosons --- is crucial for the formation of the condensed (confined) phase. We relate standard criteria, based on off-diagonal long range order (ODLRO) for BEC and the Polyakov loop for gauge theory. The constant offset of the distribution of the phases of the Polyakov loop corresponds to ODLRO, and gives the order parameter for the partially-(de)confined phase at finite coupling. Furthermore we show the numerical evidence for this phenomenon at strong coupling, by using the Yang-Mills matrix model as a concrete example and solving it numerical via lattice simulation. This talk is based on a series of papers, especially "Color Confinement and Bose-Einstein Condensation" by Hanada, Shimada and Wintergerst, 2001.10459 [hep-th] and "Partial Deconfinement at Strong Coupling on a Lattice' by Bergner, Bodendorfer, Funai, Hanada, Rinaldi, Schaefer, Vranas and Watanabe to appear (should be in hep-th by the talk).