Entanglement Entropy of Large-NWilson-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=∞. Notably, for a semi-infinite cylindrical region it scales as N0 in the Wilson-Fisher theory, in stark contrast to the N-linear result of the Gaussian fixed point.