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 N2/4, independent of the charge of the state.
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Acknowledgments
D.B. would like to thank D. O’Connor, S. Ramgoolam for discussions and correspondence. D.B. research was supported in part by the International Centre for Theoretical Sciences (ICTS) while participating in the program - ICTS Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography (code: ICTS/numstrings-2022/9). Research supported in part by the Department of Energy under grant DE-SC 0011702.
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Berenstein, D., Yan, K. The endpoint of partial deconfinement. J. High Energ. Phys. 2023, 30 (2023). https://doi.org/10.1007/JHEP12(2023)030
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DOI: https://doi.org/10.1007/JHEP12(2023)030