Holographic entanglement entropy ofN=2*renormalization group flow

Abstract

The $\mathcal{N}={2}^{*}$ theory is obtained by deforming $\mathcal{N}=4$ supersymmetric Yang--Mills theory with two relevant operators of dimensions 2 and 3. We study the holographic entanglement entropy of the $\mathcal{N}={2}^{*}$ theory along the whole renormalization group flow. We find that in the UV the holographic entanglement entropy for an arbitrary entangling region receives a universal logarithmic correction, which is related to the relevant operator of dimension 3. This universal behavior can be interpreted on the field theory side by perturbatively evaluating the entanglement entropy of a conformal field theory (CFT) under relevant deformations. In the IR regime, we obtain the large $R$ behavior of the renormalized entanglement entropy for both a strip and a sphere entangling region, where $R$ denotes the size of the entangling region. A term proportional to $1/R$ is found for both cases, which can be attributed to the emergent ${\mathrm{CFT}}_{5}$ in the IR.