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Olga Papadoulaki, University of Southampton

FZZT branes and non-singlets of Matrix Quantum Mechanics

We will discuss the non-singlet sectors of the matrix model associated with two dimensional non-critical string theory. These sectors of the matrix model contain rich physics and are expected to describe non-trivial states such as black holes. I will present how one can turn on the non-singlets by adding $N_f \times N$ fundamental and anti-fundamental fields in the gauge matrix quantum mechanics model as well as a Chern-Simons term. Then, I will show how one can rewrite our model as a spin-Calogero model in an external magnetic field. By introducing chiral variables we can define spin-currents that in the large $N$ limit satisfy an $SU(2N_f )_k$ Kac-Moody algebra. Moreover, we can write down the canonical partition function and study different limits of the parameters and possible phase transitions. In the grand canonical ensemble the partition function is a $\tau$ - function obeying discrete soliton equations. Also, in a certain limit we recover the matrix model of Kazakov-Kostov-Kutasov conjectured to describe the two dimensional black hole. Finally, I will discuss several implications that our model has for the understanding of the thermodynamics and the physics of such string theory states.