Classical and Quantum D-branes in 2D String Theory

TL;DR

This paper explores two types of D-branes in 2D string theory, analyzing their roles during tachyon condensation and linking them to matrix model eigenvalues, revealing classical and quantum descriptions.

Contribution

It provides a detailed comparison of extended and localized D-branes in 2D string theory and their correspondence with matrix model eigenvalues and boundary states.

Findings

Extended branes correspond to classical eigenvalue trajectories.

Localized branes represent quantum fields creating and destroying eigenvalues.

The matrix model relations match the boundary state descent relations.

Abstract

We investigate two classes of D-branes in 2-d string theory, corresponding to extended and localized branes, respectively. We compute the string emission during tachyon condensation and reinterpret the results within the $c=1$ matrix model. As in hep-th/0304224, we find that the extended branes describe classical eigenvalue trajectories, while, as found in hep-th/0305159, the localized branes correspond to the quantum field that creates and destroys eigenvalues. The matrix model relation between the classical probe and the local collective field precisely matches with the descent relation between the boundary states of D-strings and D-particles.