The endpoint of partial deconfinement

• Published in: The journal of high energy physics Vol. 2023; no. 12; pp. 30 - 20
• Main Authors: Berenstein, David, Yan, Kai
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 04.12.2023; Springer Nature B.V; Springer Nature; SpringerOpen
• Subjects: 1/N Expansion; Black holes; Classical and Quantum Gravitation; Combinatorial analysis; Elementary Particles; Energy; Entropy; Gauge-Gravity Correspondence; Heat; High energy physics; Matrix Models; Phase transitions; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum mechanics; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Gauge-Gravity Correspondence; 1; Expansion; Matrix Models
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP12(2023)030

A bstract 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.