TY - JOUR

T1 - Color confinement and Bose-Einstein condensation

AU - Hanada, Masanori

AU - Shimada, Hidehiko

AU - Wintergerst, Nico

PY - 2021/8/9

Y1 - 2021/8/9

N2 - 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. We demonstrate this explicitly for several quantum mechanical systems (i.e., theories at small or zero spatial volume) at weak coupling, and argue that this mechanism extends to large volume and/or strong coupling. This viewpoint may have implications for confinement at finite N, and for quantum gravity via gauge/gravity duality.

AB - 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. We demonstrate this explicitly for several quantum mechanical systems (i.e., theories at small or zero spatial volume) at weak coupling, and argue that this mechanism extends to large volume and/or strong coupling. This viewpoint may have implications for confinement at finite N, and for quantum gravity via gauge/gravity duality.

KW - 1/N Expansion

KW - Gauge-gravity correspondence

KW - M(atrix) Theories

KW - Wilson

KW - 't Hooft and Polyakov loops

KW - PATH-INTEGRAL COMPUTATION

KW - PHASE-TRANSITION

KW - LIQUID-HELIUM

KW - ATOMIC THEORY

KW - GAUGE

KW - MODEL

U2 - 10.1007/JHEP08(2021)039

DO - 10.1007/JHEP08(2021)039

M3 - Journal article

VL - 2021

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

SN - 1126-6708

IS - 8

M1 - 039

ER -