TY - JOUR

T1 - Entanglement and RG in the O(N) vector model

AU - Akers, Chris

AU - Ben-Ami, Omer

AU - Rosenhaus, Vladimir

AU - Smolkin, Michael

AU - Yankielowicz, Shimon

N1 - Publisher Copyright:
© 2016, The Author(s).

PY - 2016/3/1

Y1 - 2016/3/1

N2 - Abstract: We consider the large N interacting vector O(N) model on a sphere in 4 − ϵ Euclidean dimensions. The Gaussian theory in the UV is taken to be either conformally or non-conformally coupled. The endpoint of the RG flow corresponds to a conformally coupled scalar field at the Wilson-Fisher fixed point. We take a spherical entangling surface in de Sitter space and compute the entanglement entropy everywhere along the RG trajectory. In 4 dimensions, a free non-conformal scalar has a universal area term scaling with the logarithm of the UV cutoff. In 4 − ϵ dimensions, such a term scales as 1/ϵ. For a non-conformal scalar, a 1/ϵ term is present both at the UV fixed point, and its vicinity. For flow between two conformal fixed points, 1/ϵ terms are absent everywhere. Finally, we make contact with replica trick calculations. The conical singularity gives rise to boundary terms residing on the entangling surface, which are usually discarded. Consistency with our results requires they be kept. We argue that, in fact, this conclusion also follows from the work of Metlitski, Fuertes, and Sachdev, which demonstrated that such boundary terms will be generated through quantum corrections.

AB - Abstract: We consider the large N interacting vector O(N) model on a sphere in 4 − ϵ Euclidean dimensions. The Gaussian theory in the UV is taken to be either conformally or non-conformally coupled. The endpoint of the RG flow corresponds to a conformally coupled scalar field at the Wilson-Fisher fixed point. We take a spherical entangling surface in de Sitter space and compute the entanglement entropy everywhere along the RG trajectory. In 4 dimensions, a free non-conformal scalar has a universal area term scaling with the logarithm of the UV cutoff. In 4 − ϵ dimensions, such a term scales as 1/ϵ. For a non-conformal scalar, a 1/ϵ term is present both at the UV fixed point, and its vicinity. For flow between two conformal fixed points, 1/ϵ terms are absent everywhere. Finally, we make contact with replica trick calculations. The conical singularity gives rise to boundary terms residing on the entangling surface, which are usually discarded. Consistency with our results requires they be kept. We argue that, in fact, this conclusion also follows from the work of Metlitski, Fuertes, and Sachdev, which demonstrated that such boundary terms will be generated through quantum corrections.

KW - Conformal and W Symmetry

KW - Global Symmetries

KW - Renormalization Group

UR - http://www.scopus.com/inward/record.url?scp=84959552487&partnerID=8YFLogxK

U2 - 10.1007/JHEP03(2016)002

DO - 10.1007/JHEP03(2016)002

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AN - SCOPUS:84959552487

SN - 1126-6708

VL - 2016

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 3

M1 - 2

ER -