Rényi entropy, stationarity, and entanglement of the conformal scalar
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13130_2015_Article_9941.pdf
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Author(s)
Lee, Jeongseog
Lewkowycz, Aitor
Perlmutter, Eric
Safdi, Benjamin Ryan
Date Issued
March 2015
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
Lee, Jeongseog et al. “Rényi Entropy, Stationarity, and Entanglement of the Conformal Scalar.” Journal of High Energy Physics 2015.3 (2015): n. pag.
Version
Final published version
Abstract
We extend previous work on the perturbative expansion of the Rényi entropy, Sq , around q = 1 for a spherical entangling surface in a general CFT. Applied to conformal scalar fields in various spacetime dimensions, the results appear to conflict with the known conformal scalar Rényi entropies. On the other hand, the perturbative results agree with known Rényi entropies in a variety of other theories, including theories of free fermions and vector fields and theories with Einstein gravity duals. We propose a resolution stemming from a careful consideration of boundary conditions near the entangling surface. This is equivalent to a proper treatment of total-derivative terms in the definition of the modular Hamiltonian. As a corollary, we are able to resolve an outstanding puzzle in the literature regarding the Rényi entropy of N=4 super-Yang-Mills near q = 1. A related puzzle regards the question of stationarity of the renormalized entanglement entropy (REE) across a circle for a (2+1)-dimensional massive scalar field. We point out that the boundary contributions to the modular Hamiltonian shed light on the previously-observed non-stationarity. Moreover, IR divergences appear in perturbation theory about the massless fixed point that inhibit our ability to reliably calculate the REE at small non-zero mass.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP03(2015)075
