Matrix models for D-particle dynamics and the string/black hole transition

TL;DR

This paper constructs matrix models for D0-branes in various 2D string backgrounds, revealing how the string/black hole transition manifests through potential changes at the Hagedorn temperature.

Contribution

It introduces a canonical transformation approach to map the Dirac-Born-Infeld action to matrix models for generic 2D backgrounds, illustrating the string/black hole transition.

Findings

Matrix models for Rindler and AdS_2 spaces with specific potentials.

At Hagedorn temperature, the matrix model matches the linear dilaton background.

The formalism encodes background geometry in the matrix potential.

Abstract

For a generic two-dimensional 0A string background, we map the Dirac-Born-Infeld action to a matrix model. This is achieved using a canonical transformation. The action describes D0-branes in this background, while the matrix model has a potential which encodes all the information of the background geometry. We apply this formalism to specific backgrounds: For Rindler space, we obtain a matrix model with an upside-down quadratic potential, while for AdS_2 space, the potential is linear. Furthermore we analyze the black hole geometry with RR flux. In particular, we show that at the Hagedorn temperature, the resulting matrix model coincides with the one for the linear dilaton background. We interpret this result as a realization of the string/black hole transition.