Open Strings On The Rindler Horizon

TL;DR

This paper explores using a Z_N orbifold to model Rindler space thermodynamics in string theory, finding that tachyons disappear after analytic continuation and suggesting the resulting theory may be a nonunitary logarithmic conformal field theory.

Contribution

It investigates the open-string sector of the orbifold approach to Rindler space thermodynamics and provides evidence for a nonunitary logarithmic conformal field theory after analytic continuation.

Findings

Tachyons vanish after analytic continuation for the relevant region.

Evidence suggests the resulting theory is a logarithmic conformal field theory.

Analytic continuation of the orbifold CFT remains a significant challenge.

Abstract

It has been proposed that a certain Z_N orbifold, analytically continued in N, can be used to describe the thermodynamics of Rindler space in string theory. In this paper, we attempt to implement this idea for the open-string sector. The most interesting result is that, although the orbifold is tachyonic for positive integer N, the tachyon seems to disappear after analytic continuation to the region that is appropriate for computing ${\mathrm {Tr}} \rho^{\mathcal N}$, where $\rho$ is the density matrix of Rindler space and Re $\mathcal N$>1. Analytic continuation of the full orbifold conformal field theory remains a challenge, but we find some evidence that if such analytic continuation is possible, the resulting theory is a logarithmic conformal field theory, necessarily nonunitary.