Open String Descriptions of Space-like Singularities in Two Dimensional String Theory

TL;DR

This paper explores how open string degrees of freedom, specifically fermions, evolve smoothly in a two-dimensional string theory background with space-like singularities, contrasting with the apparent pathology of the closed string perspective.

Contribution

It demonstrates that fermion dynamics remain well-defined and smooth despite space-like singularities in the closed string background, and provides a method for exact correlator calculations.

Findings

Fermion evolution is smooth even with space-like singularities.

Open string perspective offers a well-defined evolution contrary to closed string view.

Exact fermion correlators are computed consistent with semiclassical analysis.

Abstract

The matrix model formulation of two dimensional string theory has been shown to admit time dependent classical solutions whose closed string duals are geodesically incomplete space-times with space-like boundaries. We investigate some aspects of the dynamics of fermions in one such background. We show that even though the background solution appears pathological, the time evolution of the system is smooth in terms of open string degrees of freedom, viz. the fermions. In particular, an initial state of fermions evolves smoothly into a well defined final state over an infinite open string time interval, while the time perceived by closed strings appears to end abruptly. We outline a method of calculating fermion correlators exactly using symmetry properties. The result for the two point function is consistent with the semiclassical picture.