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arXiv:2310.13735 · Journal of High Energy Physics

Entanglement entropy in string compactifications

Atish Dabholkar A, Upamanyu Moitra

Published Jun 28, 2024• 3 citations
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Abstract

A bstract We consider ℤ N orbifolds of Type-II compactifications to four and six dimensions on several Calabi-Yau manifolds in the orbifold limit with the aim to compute the entanglement entropy. The spectrum can contain tachyons in the doubly-twisted sectors which can lead to new infrared divergences for the partition function that are not present in the orbifolds of the uncompactified ten-dimensional theory. We show that all tachyonic contributions in these models admit a resummation and analytic continuation that yields finite entropy in the physical region 0 < N ≤ 1 just as in ten dimensions.

DOI
10.1007/jhep06(2024)209

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We analyze the one-loop quantum entanglement entropy in ten-dimensional type-II string theory using the orbifold method by analytically continuing in N the genus-one partition function for string orbifolds on R 2 / Z N conical spaces known for all odd integers N > 1 . We show that the tachyonic contributions to the orbifold partition function can be appropriately summed and analytically continued to an expression that is finite in the physical region 0 < N ≤ 1 resulting in a finite and calculable answer for the entanglement entropy. We discuss the implications of the finiteness of the entanglement entropy for the information paradox, quantum gravity, and holography. Published by the American Physical Society 2024
We define entanglement entropy in string perturbation theory using the orbifold method -- a stringy analog of the replica method in field theory. To this end, we use the Newton series to analytically continue in NNN the partition functions for string orbifolds on C/ZN\mathbb{C}/\mathbb{Z}_NC/ZN​ conical spaces, known for all odd integer NNN. In the concrete example of ten-dimensional Type-IIB strings, the one-loop partition function can be computed explicitly and the one-loop entropy can be expressed as a manifestly modular invariant series in terms of the Weierstrass ℘\wp℘ function. The convergence of the series is not evident but, from physical arguments based on holography, it is expected to yield a finite answer together with the tree level contribution. This method has a natural generalization to other string compactifications and to higher genus Riemann surfaces; it can provide a modular invariant definition of generalized entropy in a given string vacuum to all orders, of potential interest for the generalized second law of thermodynamics.
A bstract We construct ℤ N orbifolds of the ten-dimensional heterotic string theories appropriate for implementing the stringy replica method for the calculation of quantum entanglement entropy. A novel feature for the heterotic string is that the gauge symmetry must be broken by a Wilson line to ensure modular invariance. We completely classify the patterns of symmetry breaking. We show that the tachyonic contributions in all cases can be analytically continued, with a finite answer in the domain 0 < N ≤ 1, relevant for calculating entanglement entropy across the Rindler horizon. We discuss the physical implications of our results.
We study the entanglement entropy for open bosonic strings on multiple Dp -branes by using the covariant open string field theory. Choosing one of the spatial coordinates which are tangential to the hyperplane on which Dp -branes are located, we divide the hyperplane into two halves. By using the string wavefunction in the Fock space representation, we evaluate the entanglement entropy. The entanglement entropy is found to be proportional to the area of ( p − 1 ) -dimensional boundary of the bipartite hyperplanes and divergent in the ultraviolet (UV) region as well as in the infrared (IR) region. However, the leading divergences are mainly due to tachyon contributions to the entanglement entropy, which may be absent in supersymmetric string theories . Apart from the divergences thanks to tachyons, the entanglement entropy for open bosonic strings on Dp -branes is finite for 2 ≤ p ≤ d critical − 2 and logarithmically divergent for p = 1 , d critical − 1 .
A bstract We study entanglement entropy in the low-energy effective field theory of two-dimensional string theory as well as in the singlet sector of the dual c = 1 matrix quantum mechanics. From the target space perspective, we argue that a generic bulk subregion is expected to have an associated generalized entanglement entropy combining a dilaton-dependent gravitational term and a matter contribution coming from the tachyon, extending the construction from black hole horizons to arbitrary subregions. Motivated by the absence of the gravitational area-like term in previous analyses of entanglement entropy in the c = 1 model, we compute the effect on the entanglement entropy of the nonlocal transformation induced by the leg-pole factor that relates the target space tachyon and the matrix model collective excitations, finding that it cannot account for the area-like term. We offer preliminary comments on the possible origin of the area term in the non-singlet sectors of the theory.
Abstract In this work we study the time evolution of the Rényi entanglement entropy for locally excited states created by twist operators in the cyclic orbifold ( T 2 ) n / Z n and the symmetric orbifold ( T 2 ) n / S n . We find that when the square of its compactification radius is rational, the second Rényi entropy approaches a universal constant equal to the logarithm of the quantum dimension of the twist operator. On the other hand, in the non-rational case, we find a new scaling law for the Rényi entropies given by the double logarithm of time log log ⁡ t for the cyclic orbifold CFT.