2 A Gravity Dual of Momentum Relaxation with Electric Field

We studied the holographic entanglement entropy for a strip and sharp wedge entangling regions in momentum relaxation systems. In the case of strips, we found analytic and numerical results for the entanglement entropy and examined the effect of the electric field on the entanglement entropy. We also studied the entanglement entropy of wedges and confirmed that there is a linear change due to the electric field. In this case, we showed that the entanglement entropy change is interestingly proportional to the thermoelectric conductivity which is a measurable quantity. Also, we discussed comparable calculations with ABJM theory and we suggested an experiment for our result. ∗ e-mail : kimkyungkiu@sejong.ac.kr † e-mail : cyong21@gist.ac.kr ‡ e-mail : junghun.lee@gist.ac.kr § e-mail : bjahn@yonsei.ac.kr ar X iv :1 80 4. 00 41 2v 2 [ he pth ] 8 J an 2 01 9