Open strings on the Rindler horizon

A bstract 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 Tr $$ {\rho}^{\mathcal{N}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>ρ</mml:mi> <mml:mi>N</mml:mi> </mml:msup> </mml:math> , where ρ is the density matrix of Rindler space and Re $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> &gt; 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.