de Sitter space and extremal surfaces for spheres

Following arXiv:1501.03019 [hep-th], we study de Sitter space and spherical subregions on a constant boundary Euclidean time slice of the future boundary in the Poincare slicing. We show that as in that case, complex extremal surfaces exist here as well: for even boundary dimensions, we isolate the universal coefficient of the logarithmically divergent term in the area of these surfaces. There are parallels with analytic continuation of the Ryu-Takayanagi expressions for holographic entanglement entropy in $AdS/CFT$. We then study the free energy of the dual Euclidean CFT on a sphere holographically using the $dS/CFT$ dictionary with a dual de Sitter space in global coordinates, and a classical approximation for the wavefunction of the universe. For even dimensions, we again isolate the coefficient of the logarithmically divergent term which is expected to be related to the conformal anomaly. We find agreement including numerical factors between these coefficients.Comment: Latex, 14pgs, v3: published version, more detailed clarifications adde

On extremal surfaces and de Sitter entropy

We study extremal surfaces in the static patch coordinatization of de Sitter space, focussing on the future and past universes. We find connected timelike codim-2 surfaces on a boundary Euclidean time slice stretching from the future boundary $I^+$ to the past boundary $I^-$. In a limit, these surfaces pass through the bifurcation region and have minimal area with a divergent piece alone, whose coefficient is de Sitter entropy in 4-dimensions. These are reminiscent of rotated versions of certain surfaces in the $AdS$ black hole. We close with some speculations on a possible $dS/CFT$ interpretation of 4-dim de Sitter space as dual to two copies of ghost-CFTs in an entangled state. For a simple toy model of two copies of ghost-spin chains, we argue that similar entangled states always have positive norm and positive entanglement.Comment: Latex, 20pgs, 3 figs, v3: clarifications added, some reorganizing of text, review of ghost-spin chains added, matches version to be published, v4: further minor clarifications adde

On the internal structure of dyons in N=4{\cal N}=4 super Yang-Mills theories

We use the low energy effective $U(1)^r$ action on the Coulomb branch of ${\cal N}=4$ super Yang-Mills theory to construct approximate field configurations for solitonic dyons in these theories, building on the brane prong description developed in hep-th/0101114. This dovetails closely with the corresponding description of these dyons as string webs stretched between D-branes in the transverse space. The resulting picture within these approximations shows the internal structure of these dyons (for fixed asymptotic charges) to be molecule-like, with multiple charge cores held together at equilibrium separations, which grow large near lines of marginal stability. Although these techniques do not yield a complete solution for the spatial structure (i.e. all core sizes and separations) of large charge multicenter dyons in high rank gauge theories, approximate configurations can be found in specific regions of moduli space, which become increasingly accurate near lines of marginal stability. We also discuss string webs with internal faces from this point of view.Comment: Latex, 29 pgs, 5 eps figures; v2: typos fixed, minor clarifications on internal face