Color Confinement and Bose-Einstein Condensation

Abstract

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.

MH would like to dedicate this paper to Keitaro Nagata, who loved QCD more than anybody else does. v2: The presentation was improved. The logic and conclusion are unchanged. v3: References were added, some discussions were elaborated, typographical errors in Appenx A were fixed. v4: Matches the version accepted for publication in JHEP

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Cited by in corpus (10)

• Quantum simulation of gauge theory via orbifold lattice
• Confinement/deconfinement transition in the D0-brane matrix model -- A signature of M-theory?
• Toward QCD on Quantum Computer: Orbifold Lattice Approach
• Matrix Entanglement
• On thermal transition in QCD
• Global Symmetries and Partial Confinement
• Partial deconfinement: a brief overview
• Linear confinement in the partially-deconfined phase
• Variational Monte Carlo with Neural Network Quantum States for Yang-Mills Matrix Model
• Multiplicity, probabilities, and canonical sectors for the cold QCD matter