AAPPS Bulletin (Dec 2021)

On the renormalization of entanglement entropy

  • Jin-Yi Pang,
  • Jiunn-Wei Chen

DOI
https://doi.org/10.1007/s43673-021-00032-1
Journal volume & issue
Vol. 31, no. 1
pp. 1 – 7

Abstract

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Abstract The renormalization of entanglement entropy of quantum field theories is investigated in the simplest setting with a λ ϕ 4 scalar field theory. The 3+1 dimensional spacetime is separated into two regions by an infinitely flat 2-dimensional interface. The entanglement entropy of the system across the interface has an elegant geometrical interpretation using the replica trick, which requires putting the field theory on a curved spacetime background. We demonstrate that the theory, and hence the entanglement entropy, is renormalizable at order λ once all the relevant operators up to dimension 4 are included in the action. This exercise has a one-to-one correspondence to entanglement entropy interpretation of the black hole entropy which suggests that our treatment is sensible. Our study suggests that entanglement entropy is renormalizable and is a physical quantity.

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