Equivariant Localization in Supergravity.

We show that supersymmetric supergravity solutions with an R-symmetry Killing vector are equipped with a set of equivariantly closed forms. Various physical observables may be expressed as integrals of these forms, and then evaluated using the Berline-Vergne-Atiyah-Bott fixed point theorem. We illustrate with a variety of holographic examples, including on-shell actions, black hole entropies, central charges, and scaling dimensions of operators. The resulting expressions depend only on topological data and the R-symmetry vector, and hence may be evaluated without solving the supergravity equations.

Entropy Functions for Accelerating Black Holes.

We introduce an entropy function for supersymmetric accelerating black holes in four-dimensional anti-de Sitter space that uplift on general Sasaki-Einstein manifolds X_{7} to solutions of M theory. This allows one to compute the black hole entropy without knowing the explicit solutions. A dual holographic microstate counting would follow from computing certain supersymmetric partition functions of Chern-Simons-matter theories compactified on a spindle. We make a general prediction for a class of such partition functions in terms of "blocks," with each block being constructed from the partition function on a three-sphere.

D3-Branes Wrapped on a Spindle.

We construct supersymmetric AdS_{3}×Σ solutions of minimal gauged supergravity in D=5, where Σ is a two-dimensional orbifold known as a spindle. Remarkably, these uplift on S^{5}, or more generally on any regular Sasaki-Einstein manifold, to smooth solutions of type IIB supergravity. The solutions are dual to d=2, N=(0,2) SCFTs and we show that the central charge for the gravity solution agrees with a field theory calculation associated with D3-branes wrapped on Σ.

Snow-mediated plasticity does not prevent camouflage mismatch.

Global reduction in snow cover duration is one of the most consistent and widespread climate change outcomes. Declining snow duration has severe negative consequences for diverse taxa including seasonally color molting species, which rely on snow for camouflage. However, phenotypic plasticity may facilitate adaptation to reduced snow duration. Plastic responses could occur in the color molt phenology or through behavior that minimizes coat color mismatch or its consequences. We quantified molt phenology of 200 wild snowshoe hares (Lepus americanus), and measured microhabitat choice and local snow cover. Similar to other studies, we found that hares did not show behavioral plasticity to minimize coat color mismatch via background matching; instead they preferred colder, snow free areas regardless of their coat color. Furthermore, hares did not behaviorally mitigate the negative consequences of mismatch by choosing resting sites with denser vegetation cover when mismatched. Importantly, we demonstrated plasticity in the initiation and the rate of the molt and established the direct effect of snow on molt phenology; greater snow cover was associated with whiter hares and this association was not due to whiter hares preferring snowier areas. However, despite the observed snow-mediated plasticity in molt phenology, camouflage mismatch with white hares on brown snowless ground persisted and was more frequent during early snowmelt. Thus, we find no evidence that phenotypic plasticity in snowshoe hares is sufficient to facilitate adaptive rescue to camouflage mismatch under climate change.

Gravity dual of supersymmetric gauge theories on a squashed five-sphere.

We present the gravity dual of large N supersymmetric gauge theories on a squashed five-sphere. The one-parameter family of solutions is constructed in Euclidean Romans F(4) gauged supergravity in six dimensions, and uplifts to massive type IIA supergravity. By renormalizing the theory with appropriate counterterms we evaluate the renormalized on-shell action for the solutions. We also evaluate the large N limit of the gauge theory partition function, and find precise agreement.

Central charge of supersymmetric 5D anti-de sitter space solutions of type IIB supergravity.

We show that generic supersymmetric 5D anti-de Sitter solutions of type IIB supergravity admit a canonical contact structure. This structure determines the central charge of the dual field theory and the conformal dimension of operators dual to supersymmetric wrapped D3-branes. Hence both quantities can be calculated using incomplete information about the solutions, allowing us to prove that they are rational numbers for solutions with a U(1) R symmetry, in agreement with field theory expectations. We also discuss related Duistermaat-Heckman integrals and localization formulas.