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}_fright)}_{tilde{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.
Highlights
The duality between the singlet sector of gauged Matrix Quantum Mechanics (MQM) and c = 1 Liouville theory is long known to provide a very powerful complementary description of the physics of this low-dimensional version of string theory
We explored a model that captures the physics of non singlet sectors of matrix quantum mechanics dual to c = 1 Liouville theory
The field content of the model is a N × N matrix that transforms in the adjoint of SU(N ) which describes the dynamics of N unstable ZZ branes and Nf ×N fundamental and anti-fundamental fields that describe the dynamics of open strings streched between the ZZ and FZZT branes
Summary
This allows a complete characterisation of the specific MQM non-singlet representations that are activated due to the extra dynamical bi-fundamental fields. In addition our analysis of the grand canonical partition function in subsection 5.4 and appendix F, shows that one can define a complex string coupling parameter through the combination μ + ik (k is a Chern-Simons level in the MQM side), that takes into account fluxes sourced by the FZZT branes This concludes our preliminary connection between matrix model and Liouville theory/ FZZT brane parameters. We discuss the relevant constraints in appendix E, but leave as a future work the task to solve them in conjuction with the discrete soliton equations
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