The endpoint of partial deconfinement

Berenstein, David; Yan, Kai

doi:10.1007/jhep12(2023)030

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The endpoint of partial deconfinement

Berenstein, David·Yan, Kai

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Abstract

We study the matrix quantum mechanics of two free hermitian N × N matrices subject to a singlet constraint in the microcanonical ensemble. This is the simplest example of a theory that at large N has a confinement/deconfinement transition. In the microcanonical ensemble, it also exhibits partial deconfinement with a Hagedorn density of states. We argue that the entropy of these configurations, based on a combinatorial counting of Young diagrams, are dominated by Young diagrams that have the VKLS shape. When the shape gets to the maximal depth allowed for a Young diagram of SU(N), namely N, we argue that the system stops exhibiting the Hagedorn behavior. The number of boxes (energy) at the transition is N 2 /4, independent of the charge of the state.

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1/N Expansion 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS Excited States Gauge-Gravity Correspondence Matrix Models Matrix Theory Phase Transition and Critical Phenomena Physics Statistical Mechanics Statistical Physics Warm and dense matter

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Berenstein, David, Yan, Kai. 2023-12-04. The endpoint of partial deconfinement. https://doi.org/10.1007/jhep12(2023)030

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