Renormalized entanglement entropy flow in mass-deformed ABJM theory

We investigate a mass deformation effect on the renormalized entanglement entropy (REE) near the UV fixed point in ($2+1$)-dimensional field theory. In the context of the gauge/gravity duality, we use the Lin-Lunin-Maldacena geometries corresponding to the vacua of the mass-deformed ABJM theory. We analytically compute the small mass effect for various droplet configurations and show in holographic point of view that the REE is monotonically decreasing, positive, and stationary at the UV fixed point. These properties of the REE in ($2+1$)-dimensions are consistent with the Zamolodchikov $c$-function proposed in ($1+1$)-dimensional conformal field theory.

Figure 1

Change of the minimal surface due to the mass deformation in the symmetric case $\tilde{\sigma }=0$.