Submatrix deconfinement and small black holes in AdS

A bstract 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.