Abstract:We consider generalized gravitational entropy in various higher derivative theories of gravity dual to four dimensional CFTs using the recently proposed regularization of squashed cones. We derive the universal terms in the entanglement entropy for spherical and cylindrical surfaces. This is achieved by constructing the Fefferman-Graham expansion for the leading order metrics for the bulk geometry and evaluating the generalized gravitational entropy. We further show that the Wald entropy evaluated in the bulk geometry constructed for the regularized squashed cones leads to the correct universal parts of the entanglement entropy for both spherical and cylindrical entangling surfaces. We comment on the relation with the Iyer-Wald formula for dynamical horizons relating entropy to a Noether charge. Finally we show how to derive the entangling surface equation in Gauss-Bonnet holography.

In arXiv:1310.5713 [1] and arXiv:1310.6659 [2] a formula was proposed as the entanglement entropy functional for a general higher-derivative theory of gravity, whose lagrangian consists of terms containing contractions of the Riemann tensor. In this paper, we carry out some tests of this proposal. First, we find the surface equation of motion for general four-derivative gravity theory by minimizing the holographic entanglement entropy functional resulting from this proposed formula. Then we calculate the surface equation for the same theory using the generalized gravitational entropy method of arXiv:1304.4926 [3]. We find that the two do not match in their entirety. We also construct the holographic entropy functional for quasi-topological gravity, which is a six-derivative gravity theory. We find that this functional gives the correct universal terms. However, as in the four-derivative case, the generalized gravitational entropy method applied to this theory does not give exactly the surface equation of motion coming from minimizing the entropy functional.

According to the standard prescriptions, zero-temperature string theories can be extended to finite temperature by compactifying their time directions on a so-called "thermal circle" and implementing certain orbifold twists. However, the existence of a topologically non-trivial thermal circle leaves open the possibility that a gauge flux can pierce this circle -i.e., that a non-trivial Wilson line (or equivalently a non-zero chemical potential) might be involved in the finite-temperature extension. In this paper, we concentrate on the zero-temperature heterotic and Type I strings in ten dimensions, and survey the possible Wilson lines which might be introduced in their finite-temperature extensions. We find a rich structure of possible thermal string theories, some of which even have non-traditional Hagedorn temperatures, and we demonstrate that these new thermal string theories can be interpreted as extrema of a continuous thermal free-energy "landscape". Our analysis also uncovers a unique finite-temperature extension of the heterotic SO(32) and E8 × E8 strings which involves a non-trivial Wilson line, but which -like the traditional finite-temperature extension without Wilson lines -is metastable in this thermal landscape.