Abstract
We argue that the confined and deconfined phases in gauge theories are connected by a partially deconfined phase (i.e. SU(M) in SU(N), where M < N, is deconfined), which can be stable or unstable depending on the details of the theory. When this phase is unstable, it is the gauge theory counterpart of the small black hole phase in the dual string theory. Partial deconfinement is closely related to the Gross-Witten-Wadia transition, and is likely to be relevant to the QCD phase transition.The mechanism of partial deconfinement is related to a generic property of a class of systems. As an instructive example, we demonstrate the similarity between the Yang-Mills theory/string theory and a mathematical model of the collective behavior of ants [Beekman et al., Proceedings of the National Academy of Sciences, 2001]. By identifying the D-brane, open string and black hole with the ant, pheromone and ant trail, the dynamics of two systems closely resemble with each other, and qualitatively the same phase structures are obtained.
Highlights
Figure 1. [Left] The phase structure of 4D N = 4 SYM on S3
Partial deconfinement is closely related to the Gross-Witten-Wadia transition, and is likely to be relevant to the QCD phase transition
When the black hole is much smaller than the curvature scale of AdS5×S5, it is approximately the same as the Schwarzschild black hole in ten spacetime dimensions, and E ∼ N 2T −7. This small black hole phase is interesting, in part because it provides a microscopic description of black holes with negative specific heat, which is a proxy for evaporating black holes
Summary
If the inflow/outflow wins when Ntrail is varied slightly upwards/downwards from the saddle, the saddle is unstable (dashed line in the left panel of figure 2) If the inflow/outflow wins when NBH is varied slightly upwards/downwards from the saddle, the saddle is unstable (the dashed line in the left panels of figure 3 and figure 4) In order for this to happen, the strings have to bind D-branes tighter, so the strong coupling dynamics is needed. The unstable saddle exhibits the negative specific heat because at higher temperature each open string mode can be excited more (each ant contributes to more pheromone) and strong enough attraction (strong enough pheromone) resisting the emission of D-branes (outflow of the ants) can be achieved with smaller value of NBH.
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