FZZT branes and non-singlets of matrix quantum mechanics

Abstract

Abstract We explore the non-singlet sector of matrix quantum mechanics dual to c = 1 Liouville theory. The non-singlets are obtained by adding Nf× N bi-fundamental fields in the gauged matrix quantum mechanics model as well as a one dimensional Chern-Simons term. The present model is associated with a spin-Calogero model in the presence of an external magnetic field. In chiral variables, the low energy excitations-currents satisfy an SU$$ {\left(2{N}_f\right)}_{\tilde{k}} $$ 2 N f k ˜ Kăc-Moody algebra at large N. We analyse the canonical partition function as well as two and four point correlation functions, discuss a Gross-Witten-Wadia phase transition at large N, Nf and study different limits of the parameters that allow us to recover the matrix model of Kazakov-Kostov-Kutasov conjectured to describe a two dimensional black hole. The grand canonical partition function is a τ- function obeying discrete soliton equations. We finally conjecture a possible dynamical picture for the formation of a black hole in terms of condensation of long-strings in the strongly coupled region of the Liouville direction.