Abstract
It has been proposed that a certain ℤN 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}} , where ρ 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.
Highlights
To the half-plane Re N ≥ 1, bounded by 1
It has been proposed that a certain ZN orbifold, analytically continued in N, can be used to describe the thermodynamics of Rindler space in string theory
The most interesting result is that, 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 ρN, where ρ is the density matrix of Rindler space and Re N > 1
Summary
The 1-loop amplitude for open strings is computed using a worldsheet that is an annulus. We can view the orbifold partition function on the annulus as a sum of residues of the function KJ at the poles of K on the cylinder: Resz=k/N (K(z, N )J (z, τ )). For Re z = 1/2, K2(z, N ) is the unique continuation of K(z, N ) from positive odd integer values of N that is holomorphic in the half-plane Re N > 1 and satisfies the appropriate exponential bounds. It is conceivable that this was not the best choice
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