Submatrix deconfinement and small black holes in AdS

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 N2 at the critical temperature. This paper studies the microcanonical ensemble of the model at intermediate energies 1 ≪ E ≪ N2 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 M2 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.