Relevant perturbation of entanglement entropy of singular surfaces

TL;DR

This paper investigates how relevant perturbations in conformal field theories affect the entanglement entropy of regions with singular boundaries, revealing new universal logarithmic and double logarithmic terms influenced by the perturbation's scaling dimension.

Contribution

It demonstrates that relevant perturbations introduce new universal logarithmic and double logarithmic terms in the entanglement entropy of singular surfaces, extending known results from smooth cases.

Findings

Relevant perturbations add new logarithmic terms to entanglement entropy.

Universal double logarithmic terms can appear depending on dimensions.

The scaling dimension of the relevant operator influences the entanglement entropy structure.

Abstract

We study the entanglement entropy of theories that are derived from relevant perturbation of given CFTs for regions with a singular boundary by using the AdS/CFT correspondence. In the smooth case, it is well known that a relevant deformation of the boundary theory by the relevant operator with scaling dimension $\Delta=\frac{d+2}{2}$ generates a logarithmic universal term to the entanglement entropy. As the smooth case, when the boundary CFT deformed by a relevant operator, we find that the entanglement entropy of singular surface also contains a new logarithmic term which is due to relevant perturbation of the conformal field theory, and depends on the scaling dimension of relevant operator. We also find for extended singular surfaces, $c_{n}\times R^{m}$, as well as logarithmic term, the new universal double logarithmic terms may appear depending on the scaling dimension of relevant operator and spacetime dimensions. These new terms are due to relevant perturbation of the boundary theory.