Submatrix deconfinement and small black holes in AdS

TL;DR

This work investigates confinement/deconfinement transitions in large-N gauged matrix quantum mechanics through microcanonical analysis, revealing a robust partial deconfinement phase where a submatrix of size $n_{eff} \sim \sqrt{E}$ carries the entropy. It presents two complementary counting schemes— long-trace (string) counting and Young-diagram (representation-theoretic) counting—both leading to a dominant deconfined sector of size $n_{eff} \times n_{eff}$. In the AdS/CFT context, this partial deconfinement corresponds to a small, localized black hole in $AdS_5\times S^5$, with symmetry breaking $SO(6)\to SO(5)$ and a smooth string–black-hole transition per the Susskind–Horowitz–Polchinski correspondence. The results bridge field-theoretic state counting and holographic duals, supporting the interpretation of small black holes as dual to submatrix deconfined sectors and motivating further refinement of the dynamics of the emergent submatrix degrees of freedom.

Abstract

Large $N$ gauged multi-matrix quantum mechanical models usually have a first order Hagedorn transition, related to deconfinement. In this transition the change of the energy and entropy is of order $N^2$ at the critical temperature. This paper studies the microcanonical ensemble of the model at intermediate energies $1<<E<<N^2$ in the coexistence region for the first order phase transition. Evidence is provided for a partial deconfinement phase where submatrix degrees of freedom for a $U(M)$ subgroup of $U(N)$, with $M<<N$ have an excitation energy of order $M^2$ and are effectively phase separated from the other degrees of freedom. These results also provide a simple example of the Susskind-Horowitz-Polchinski correspondence principle where a transition from a long string to a black hole is smooth. Implications for the dual configurations of small black holes in $AdS$ are discussed.

Figures (1)

• Figure 1: One the left, at weak coupling there is no cost in energy to have long magnons. One the right, at strong coupling the magnons are short and the string localizes.