Large N phase transitions and the fate of small Schwarzschild-AdS black holes

121

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.

Section: Conclusion and Discussionmentioning

confidence: 64%

Partial Deconfinement

Hanada

Ishiki

Watanabe

2019

121

“…ref. [18]), and a proposal regarding the gauge theory description [19]. Our numerical analyses in this paper are not precise enough to see such fine structure, even if it exists.…”

Section: Motivation From Gravitymentioning

confidence: 72%

Partial deconfinement at strong coupling on the lattice

Watanabe

Bergner²,

Bodendorfer

et al. 2021

We provide evidence for partial deconfinement — the deconfinement of a SU(M) subgroup of the SU(N) gauge group — by using lattice Monte Carlo simulations. We take matrix models as concrete examples. By appropriately fixing the gauge, we observe that the M × M submatrices deconfine. This gives direct evidence for partial deconfinement at strong coupling. We discuss the applications to QCD and holography.

“…It is interesting to note that for this particular branch of lumpy black holes, the microcanonical and the canonical ensembles seem to give slightly different results. This minor observation adds to the puzzles raised in [38] related to the apparent differences between the two ensembles in the thermodynamic limit.…”

Section: Jhep05(2021)265mentioning

confidence: 80%

Critical lumpy black holes in AdSp×Sq

Cardona

Figueras

2021

In this paper we study lumpy black holes with AdSp × Sq asymptotics, where the isometry group coming from the sphere factor is broken down to SO(q). Depending on the values of p and q, these are solutions to a certain Supergravity theory with a particular gauge field. We have considered the values (p, q) = (5, 5) and (p, q) = (4, 7), corresponding to type IIB supergravity in ten dimensions and eleven-dimensional supergravity respectively. These theories presumably contain an infinite spectrum of families of lumpy black holes, labeled by a harmonic number ℓ, whose endpoints in solution space merge with another type of black holes with different horizon topology. We have numerically constructed the first four families of lumpy solutions, corresponding to ℓ = 1, 2+, 2− and 3. We show that the geometry of the horizon near the merger is well-described by a cone over a triple product of spheres, thus extending Kol’s local model to the present asymptotics. Interestingly, the presence of non-trivial fluxes in the internal sphere implies that the cone is no longer Ricci flat. This conical manifold accounts for the geometry and the behavior of the physical quantities of the solutions sufficiently close to the critical point. Additionally, we show that the vacuum expectation values of the dual scalar operators approach their critical values with a power law whose exponents are dictated by the local cone geometry in the bulk.