Perturbative computation of string one-loop corrections to Wilson loop minimal surfaces in AdS(5) x S-5

We revisit the computation of the 1-loop string correction to the “latitude” minimal surface in AdS 5 × S 5 representing 1/4 BPS Wilson loop in planar N=4 SYM theory previously addressed in arXiv:1512.00841 and arXiv:1601.04708. We resolve the problem of matching with the subleading term in the strong coupling expansion of the exact gauge theory result (derived previously from localization) using a different method to compute determinants of 2d string fluctuation operators. We apply perturbation theory in a small parameter (angle of the latitude) corresponding to an expansion near the AdS 2 minimal surface representing 1/2 BPS circular Wilson loop. This allows us to compute the corrections to the heat kernels and zeta-functions of the operators in terms of the known heat kernels on AdS 2. We apply the same method also to two other examples of Wilson loop surfaces: generalized cusp and k-wound circle

Holographic entanglement entropy in AdS4/BCFT3 and the Willmore functional

We study the holographic entanglement entropy of spatial regions having arbitrary shapes in the AdS4/BCFT3 correspondence with static gravitational backgrounds, focusing on the subleading term with respect to the area law term in its expansion as the UV cutoff vanishes. An analytic expression depending on the unit vector normal to the minimal area surface anchored to the entangling curve is obtained. When the bulk spacetime is a part of AdS4, this formula becomes the Willmore functional with a proper boundary term evaluated on the minimal surface viewed as a submanifold of a three dimensional flat Euclidean space with boundary. For some smooth domains, the analytic expressions of the finite term are reproduced, including the case of a disk disjoint from a boundary which is either flat or circular. When the spatial region contains corners adjacent to the boundary, the subleading term is a logarithmic divergence whose coefficient is determined by a corner function that is known analytically, and this result is also recovered. A numerical approach is employed to construct extremal surfaces anchored to entangling curves with arbitrary shapes. This analysis is used both to check some analytic results and to find numerically the finite term of the holographic entanglement entropy for some ellipses at finite distance from a flat boundary