Microstates of a $2d$ Black Hole in string theory

TL;DR

This paper investigates matrix quantum mechanics models with non-singlet states, revealing how different parameters lead to dual geometries like long string condensates or 2D black holes, and identifying their microstates.

Contribution

It introduces a framework to analyze non-singlet states in matrix models, connecting them to 2D black holes and long string phases, and explores their microstates.

Findings

Identification of microstates from non-trivial representations.

Connection between model parameters and dual geometries.

Ability to tune parameters to explore different phases.

Abstract

We analyse models of Matrix Quantum Mechanics in the double scaling limit that contain non-singlet states. The finite temperature partition function of such systems contains non-trivial winding modes (vortices) and is expressed in terms of a group theoretic sum over representations. We then focus in the case when the first winding mode is dominant (model of Kazakov-Kostov-Kutasov). In the limit of large representations (continuous Young diagrams), and depending on the values of the parameters of the model such as the compactification radius and the string coupling, the dual geometric background corresponds to that of a long string (winding mode) condensate or a $2d$ (non-supersymmetric) Black Hole. In the matrix model we can tune these parameters and explore various phases and regimes. Our construction allows us to identify the origin of the microstates of these backgrounds, arising from non trivial representations, and paves the way for computing various observables on them.