Spacelike boundaries from thec=1matrix model

Abstract

We find classical solutions of two dimensional noncritical string theory which give rise to geometries with spacelike boundaries, similar to spacetimes with cosmological event horizons. In the c = 1 matrix model, these solutions have a representation as simple time dependent configurations. We obtain the causal structure of the resulting spacetimes. Using the macroscopic loop transform, we probe the form of the tachyon condensate in the asymptotic regions.

Open string descriptions of spacelike singularities in two dimensional string theory

“…The present paper deals with one particular background in [1]. The methods and results are, however, expected to be similar for the other backgrounds discussed in that paper.…”

“…The same fact might also suggest that there is no well defined scattering problem. The analysis of [1] however showed that the "space" on which the closed string modes propagate is related to the space of eigenvalues in a non-trivial time dependent way. As a result, this closed string space is still of infinite extent at arbitrarily late times and there is indeed a well posed scattering problem.…”

“…In [1] it was shown that there is a class of backgrounds whose closed string intepretation involve space-times with a space-like boundary. In these latter backgrounds, the time of the matrix model -which we call the open string time -runs over the full range −∞ < t < ∞.…”

“…In Section 2, we review the background solution and the behavior of collective field fluctuations at the linearized level described in [1]. Section 3 describes some aspects of the classical dynamics of small ripples on the fermi sea using the exact fermion equations of motion, following [16,17].…”

“…These include backgrounds in the matrix model formulation of two dimensional string theory which lead to spacelike boundaries in the closed string interpretation [1], ten dimensional backgrounds which admit a Matrix Theory type formulation [2,3,4,5], and deformations of AdS space-times which admit a dual gauge theory description [6,7]. In all these examples, (which build on a large body of earlier work on strings on time dependent background [8]), the low energy space-time description breaks down at the singularity as expected.…”