TY - JOUR
T1 - Shape dependence of entanglement entropy in conformal field theories
AU - Faulkner, Thomas
AU - Leigh, Robert G.
AU - Parrikar, Onkar
N1 - Publisher Copyright:
© 2016, The Author(s).
PY - 2016/4/1
Y1 - 2016/4/1
N2 - Abstract: We study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on (Formula presented.). 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 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 CT 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 (Formula presented.) in d = 3 CFTs, and the holographic Mezei formula for entanglement entropy across deformed spheres.
AB - Abstract: We study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on (Formula presented.). 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 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 CT 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 (Formula presented.) in d = 3 CFTs, and the holographic Mezei formula for entanglement entropy across deformed spheres.
KW - AdS-CFT Correspondence
KW - Field Theories in Higher Dimensions
UR - http://www.scopus.com/inward/record.url?scp=84963837767&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84963837767&partnerID=8YFLogxK
U2 - 10.1007/JHEP04(2016)088
DO - 10.1007/JHEP04(2016)088
M3 - Article
AN - SCOPUS:84963837767
SN - 1126-6708
VL - 2016
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 4
M1 - 88
ER -