On Consistent Boundary Conditions for c=1 String Theory

TL;DR

This paper introduces a new parametrisation for the $c=1$ matrix model's Fermi sea, simplifying the derivation of the scattering matrix and boundary corrections, and discusses implications for boundary conditions and black holes in $c=1$ string theory.

Contribution

It proposes a relativistic chiral field parametrisation for the $c=1$ matrix model, enabling simpler calculations of scattering and boundary effects.

Findings

Derived a simple scattering matrix using the new parametrisation

Calculated boundary corrections following Polchinski's work

Proposed a consistent set of boundary conditions for the model

Abstract

We introduce a new parametrisation for the Fermi sea of the $c = 1$ matrix model. This leads to a simple derivation of the scattering matrix, and a calculation of boundary corrections in the corresponding $1+1$--dimensional string theory. The new parametrisation involves relativistic chiral fields, rather than the non-relativistic fields of the usual formulations. The calculation of the boundary corrections, following recent work of Polchinski, allows us to place restrictions on the boundary conditions in the matrix model. We provide a consistent set of boundary conditions, but believe that they need to be supplemented by some more subtle relationship between the space-time and matrix model. Inspired by these boundary conditions, some thoughts on the black hole in $c=1$ string theory are presented.