Relevant Perturbation of Entanglement Entropy and Stationarity

Understand

A relevant perturbation of the entanglement entropy of a sphere is examined holographically near the UV fixed point.

• Varying the conformal dimension of the relevant operator, we obtain three different sectors: 1) the entanglement entropy is stationary and the perturbative expansion is well-defined with respect to the relevant coupling, 2) the entropy is stationary, but the perturbation fails, 3) the entropy is neither stationary nor perturbative.
• We compare our holographic results with the numerical calculation for a free massive scalar field in three-dimensions, and find a qualitative agreement between them.
• We speculate that these statements hold for any relevant perturbation in any quantum field theory invariant under the Poincare symmetry.