Entanglement entropy at strong coupling

Abstract

We analyze the entanglement entropy of a spherical region in N = 4 SYM theory in the strong coupling limit at zero and finite temperature. In this limit, we can apply Gauge/String duality so that the entropy is determined by the surface of minimal area in the dual gravity space such that its intersection with the boundary corresponds to the aforementioned sphere. We find the shape of the minimal surface in terms of the radius of the sphere, compute its area and examine its divergence and regularization. Finally, at nonzero temperature, we study how the regularized entanglement entropy compares to the thermal entropy as the volume of the sphere grows. We obtain that for spheres of radius ~ 1=T the entanglement entropy is about half of the thermal entropy. As the radius grows, these two entropies approach one another and for radii as large as 10=πT this deviation is still at the 10% level.