Shape dependence of entanglement entropy in conformal field theories

Journal Article · Thu Apr 14 00:00:00 EDT 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP04(2016)088· OSTI ID:1395545

Faulkner, Thomas ^[1]; Leigh, Robert G. ^[1]; Parrikar, Onkar ^[1]

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1. Univ. of Illinois, Urbana, IL (United States), Dept. of Physics

Here, we study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on R^1,d--1. We consider the entanglement entropy across a deformed planar or spherical entangling surface in terms of a perturbative expansion in the infinitesimal shape deformation. In particular, we focus on the second order term in this expansion, known as the entanglement density. This quantity is known to be non-positive by the strong-subadditivity property. We also show from a purely field theory calculation that the non-local part of the entanglement density in any CFT is universal, and proportional to the coefficient C_T appearing in the two-point function of stress tensors in that CFT. As applications of our result, we prove the conjectured universality of the corner term coefficient σ/CT=π²/24 in d = 3 CFTs, and the holographic Mezei formula for entanglement entropy across deformed spheres.

• Research Organization: Univ. of Illinois at Urbana-Champaign, IL (United States)
• Sponsoring Organization: USDOE; National Science Foundation (NSF)
• Grant/Contract Number: FG02-13ER42001; SC0009932
• OSTI ID: 1395545
• Journal Information: Journal of High Energy Physics (Online), Vol. 2016, Issue 4; ISSN 1029-8479
• Publisher: Springer Berlin
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AdS-CFT correspondence
field theories in higher dimensions