Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory

Abstract

We compute the entanglement entropy of the Wilson-Fisher conformal field theory (CFT) in 2+1 dimensions with O($N$) symmetry in the limit of large $N$ for general entanglement geometries. We show that the leading large $N$ result can be obtained from the entanglement entropy of $N$ Gaussian scalar fields with their mass determined by the geometry. For a few geometries, the universal part of the entanglement entropy of the Wilson-Fisher CFT equals that of a CFT of $N$ massless scalar fields. However, in most cases, these CFTs have a distinct universal entanglement entropy even at $N=\infty$. Notably, for a semi-infinite cylindrical region it scales as $N^0$, in stark contrast to the $N$-linear result of the Gaussian fixed point.

(v3) 23 pages, 3 figures. Published version. Added references, minor corrections and clarifications

References in corpus (11)

• Holographic c-theorems in arbitrary dimensions
• Seeing a c-theorem with holography
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Entanglement Entropy in the O(N) model
• Universality of corner entanglement in conformal field theories
• Universal entanglement entropy in 2D conformal quantum critical points
• Universal Behavior of Entanglement in 2D Quantum Critical Dimer Models
• Scaling of entanglement in $2+1$-dimensional scale-invariant field theories
• Boundary Conformal Field Theory and Entanglement Entropy in Two-Dimensional Quantum Lifshitz Critical Point
• Yukawa CFTs and Emergent Supersymmetry
• Shape dependence of two-cylinder Renyi entropies for free bosons on a lattice

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