SciPost Submission Page
Color Confinement and Bose-Einstein Condensation
by Masanori Hanada, Hidehiko Shimada, Nico Wintergerst
|As Contributors:||Nico Wintergerst|
|Arxiv Link:||https://arxiv.org/abs/2001.10459v3 (pdf)|
|Date submitted:||2020-07-22 22:32|
|Submitted by:||Wintergerst, Nico|
|Submitted to:||SciPost Physics|
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. This viewpoint may have implications for confinement at finite $N$, and for quantum gravity via gauge/gravity duality.
List of changes
- Expanded discussion after Eq.(1)
- Expanded discussion of large-N volume independence on pg. 22
- Typos corrected in Appendix A
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 1 on 2020-7-23 Invited Report
I don't have very much to add to my original report. I tried to make
a constructive suggestion about relating deconfinement and BEC of a
scalar field by bringing up the Svetitsky-Yaffe results, but it sounds
like the authors don't agree that there's any relation to what they're
saying. That's fine. But I still don't understand how to make sense
of their claims.
In their reply, the authors seem to suggest that all they want to do
is draw an analogy between BEC transitions in the thermodynamic limit,
and the deconfimenent transition of infinite-N gauge theory in finite
volume. (The manuscript speculates about finite-N extensions of the
I am certainly aware that the large N limit is a thermodynamic limit.
But in large N gauge theory the deconfinment phase transition is
always very strongly first order. But BEC transitions could be
either first or second order. The fact *even the order* of the
transition is doesn't agree between deconfinement and BEC is a loud
signal that any analogy between the systems is being pushed too far.
Moreover, I have to insist that the essense of superfluidity is the
existence of a gapless Nambu-Goldstone boson excitation in the
superfluid phase. It arises because of the spontaneous breaking of
U(1) particle number symmetry. The NGB is responsible for almost all
of the interesting phenomenology of superfluids. There's no such NGB
in gauge theory, either in the confined or deconfined phases.
Confinement famously comes with a mass gap (except when continuous
global symmetries unconnected to confinement are spontaneously
broken.) This is again a loud signal that the analogy the authors try
to draw is being pushed way too far.