Equivariant localization and holography

We discuss the theory of equivariant localization focussing on applications relevant for holography. We consider geometries comprising compact and non-compact toric orbifolds, as well as more general non-compact toric Calabi-Yau singularities. A key object in our constructions is the equivariant volume, for which we describe two methods of evaluation: the Berline-Vergne fixed-point formula and the Molien- Weyl formula, supplemented by the Jeffrey-Kirwan prescription. We present two applications in supersymmetric field theories. Firstly, we describe a method for integrating the anomaly polynomial of SCFTs on compact toric orbifolds. Secondly, we discuss equivariant orbifold indices that are expected to play a key role in the computation of supersymmetric partition functions. In the context of supergravity, we propose that the equivariant volume can be used to characterise universally the geometry of a large class of supersymmetric solutions. As an illustration, we employ equivariant localization to prove various gravitational block formulas, recovering previous results as well as obtaining generalizations.Comment: 69 pages, 10 figure

Numerical and Experimental Analysis of a CPV/T Receiver Suitable for Low Solar Concentration Factors

AbstractSolar energy conversion is one promising technology to provide the building required energy. Generally, the main used technologies are the PV and thermal flat panels, but this situation provides separately electricity and thermal energy. Electrical and Thermal power combined production is available for the concentrating solar but, usually, this technology is applied to devices working at high concentration factor (over 100), which are large and, therefore, are not suitable for roof installations. At lower concentrating factors (less of 50 suns) small linear, mono-axial, roof integrated devices can be designed and built. The solar receiver plays a key role in the performance of energy generation because it houses the solar cells and itis used to recover the thermal solar power: actually, this is the device where solar energy is converted in electrical and thermal power. The radiation flux distribution on the receiver affects the efficiency of the linear solar concentrator system, because in a mono-axial sunrays are not perpendicular to the receiver. This paper describes the numerical and experimental investigation useful to evaluate the performance of a linear low (20 suns) CPV device and to understand the thermal working condition of the solar receiver. The experimental study focuses to a quantitative analysis of the energy transfer from sun to the water. The numerical activity is a CFD conjugate analysis where the solid volume and the fluids are investigated together; the scope is to individuate how the energy flux cross the device