Rolling Tachyon Boundary State, Conserved Charges and Two Dimensional String Theory

TL;DR

This paper investigates the structure of the boundary state for rolling tachyon solutions, revealing how conserved charges are encoded and related to symmetries in two-dimensional string theory and matrix models.

Contribution

It demonstrates that the time-dependent parts of the boundary state are determined by BRST invariance and correspond to conserved charges linked to discrete states.

Findings

Conserved charges are encoded in the boundary state structure.

These charges correspond to symmetry generators in the matrix model.

The boundary state analysis applies to two-dimensional string theory.

Abstract

The boundary state associated with the rolling tachyon solution on an unstable D-brane contains a part that decays exponentially in the asymptotic past and the asymptotic future, but it also contains other parts which either remain constant or grow exponentially in the past or future. We argue that the time dependence of the latter parts is completely determined by the requirement of BRST invariance of the boundary state, and hence they contain information about certain conserved charges in the system. We also examine this in the context of the unstable D0-brane in two dimensional string theory where these conserved charges produce closed string background associated with the discrete states, and show that these charges are in one to one correspondence with the symmetry generators in the matrix model description of this theory.