Gravity duals of supersymmetric gauge theories on three-manifolds

We study gravity duals to a broad class of N=2 supersymmetric gauge theories defined on a general class of three-manifold geometries. The gravity backgrounds are based on Euclidean self-dual solutions to four-dimensional gauged supergravity. As well as constructing new examples, we prove in general that for solutions defined on the four-ball the gravitational free energy depends only on the supersymmetric Killing vector, finding a simple closed formula when the solution has U(1) x U(1) symmetry. Our result agrees with the large N limit of the free energy of the dual gauge theory, computed using localization. This constitutes an exact check of the gauge/gravity correspondence for a very broad class of gauge theories with a large N limit, defined on a general class of background three-manifold geometries.Comment: 74 pages, 2 figures; v2: minor change

A note on dimer models and McKay quivers

We give one formulation of an algorithm of Hanany and Vegh which takes a lattice polygon as an input and produces a set of isoradial dimer models. We study the case of lattice triangles in detail and discuss the relation with coamoebas following Feng, He, Kennaway and Vafa.Comment: 25 pages, 35 figures. v3:completely rewritte

Holographic renormalization and supersymmetry

Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N = 2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges.Comment: 70 pages; corrected typo

Von Neumann's expanding model on random graphs

Within the framework of Von Neumann's expanding model, we study the maximum growth rate r achievable by an autocatalytic reaction network in which reactions involve a finite (fixed or fluctuating) number D of reagents. r is calculated numerically using a variant of the Minover algorithm, and analytically via the cavity method for disordered systems. As the ratio between the number of reactions and that of reagents increases the system passes from a contracting (r1). These results extend the scenario derived in the fully connected model (D\to\infinity), with the important difference that, generically, larger growth rates are achievable in the expanding phase for finite D and in more diluted networks. Moreover, the range of attainable values of r shrinks as the connectivity increases.Comment: 20 page

Assessment of Orchid Surfaces Using Top-Down Contact Angle Mapping

© 2013 IEEE. Top-down contact angle (CA) measurements are used to characterize the green leaves and purple flowers of both old and young the Cattleya warneri orchids. The top-down CA allows the characterization of large surfaces away from the leaf edge, avoiding traditional cutting required for side view CA measurement. This allows large area mapping without damaging leaves making the method amenable to fieldwork and useful in environmental diagnostics. Young leaves are found to be hydrophobic whilst old leaves become practically hydrophilic across their entirety, mostly as a result of continued exposure to changes in the environment over time. The flowers are hydrophobic because of their visual and tactile attractor function for pollinating animals and the self-cleaning of dirt and pathogens. Real-time measurement and mapping of CA of surfaces open a new tool to assess the long-term impact of plant aging, pollution, and more of organisms in the field. The method has clear applications elsewhere such as in industrial probing of surfaces and products