Color confinement and Bose-Einstein condensation

We propose a unified description of two important phenomena: color confinement in large-$N$ gauge theory, and Bose-Einstein condensation (BEC). focus on the confinement/deconfinement transition characterized by increase entropy from $N^0$ to $N^2$, which persists weak coupling region. Indistinguishability associated with symmetry group -- SU($N$) or O($N$) S$_N$ permutations system identical bosons is crucial for formation condensed (confined) phase. relate standard criteria, based off-diagonal long range order (ODLRO) BEC Polyakov loop theory. The constant offset distribution phases corresponds ODLRO, gives parameter partially-(de)confined phase at finite coupling. demonstrate this explicitly several quantum mechanical systems (i.e., theories small zero spatial volume) coupling, argue that mechanism extends large volume and/or strong This viewpoint may have implications $N$, gravity via gauge/gravity duality.