Abstract
In this paper, we study the entanglement entropy in string theory in the simplest setup of dividing the nine dimensional space into two halves. This corresponds to the leading quantum correction to the horizon entropy in string theory on the Rindler space. This entropy is also called the conical entropy and includes surface term contributions. We first derive a new simple formula of the conical entropy for any free higher spin fields. Then we apply this formula to computations of conical entropy in open and closed superstring. In our analysis of closed string, we study the twisted conical entropy defined by making use of string theory on Melvin backgrounds. This quantity is easier to calculate owing to the folding trick. Our analysis shows that the entanglement entropy in closed superstring is UV finite owing to the string scale cutoff.
Highlights
Sa is the spin of SO(2) ⊂ SO(D) which is the rotation of (x0, x1) plane. In this way we find that the basic summation formula which we can employ to calculate the entanglement entropy for free bosons is
The conical entropy is defined as the entanglement entropy computed by using the replica method and it is not guaranteed to be positive as it includes the surface term contributions
In terms of black hole entropy for the Rindler horizon, our conical entropy from string theory one-loop amplitudes corresponds to the leading quantum corrections [20]
Summary
Before we start to analyze conical entropy (EE) in string theory, we would like to study the EE in free field theories with arbitrary spins using the first quantization approach. We express the partition function of a free field theory on the spacetime M at the first quantized level as Zf (M ). In the second quantization approach, this corresponds to the logarithm of partition function Zs(M ) We especially take a free field theory on the D dimensional flat space M = RD, whose coordinate denoted by (x0, x1, · · ·, xD−1). Combining (x0, x1) into a complex plane C, we can introduce the n-th Renyi entanglement entropy (REE) , denoted by SA(n), via an analytic continuation n = 1/N from the orbifolds C/ZN as follows (refer to [48])
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