Aspects of the moduli space of instantons on CP2\mathbb{C}P^2 and its orbifolds

We study the moduli space of self-dual instantons on $\mathbb{C}P^2$. These are described by an ADHM-like construction which allows to compute the Hilbert series of the moduli space. The latter has been found to be blind to certain compact directions. In this paper we probe these, finding them to correspond to a Grassmanian, upon considering appropriate ungaugings. Moreover, the ADHM-like construction can be embedded into a $3d$ gauge theory with a known gravity dual. Using this, we realize in $AdS_4/CFT_3$ (part of) the instanton moduli space providing at the same time further evidence supporting the $AdS_4/CFT_3$ duality. Moreover, upon orbifolding, we provide the ADHM-like construction of instantons on $\mathbb{C}P^2/\mathbb{Z}_n$ as well as compute its Hilbert series. As in the unorbifolded case, these turn out to coincide with those for instantons on $\mathbb{C}^2/\mathbb{Z}_n$.Comment: 65 page

Rigid Supersymmetry from Conformal Supergravity in Five Dimensions

We study the rigid limit of 5d conformal supergravity with minimal supersymmetry on Riemannian manifolds. The necessary and sufficient condition for the existence of a solution is the existence of a conformal Killing vector. Whenever a certain $SU(2)$ curvature becomes abelian the backgrounds define a transversally holomorphic foliation. Subsequently we turn to the question under which circumstances these backgrounds admit a kinetic Yang-Mills term in the action of a vector multiplet. Here we find that the conformal Killing vector has to be Killing. We supplement the discussion with various appendices.Comment: 23 page

Non-connected gauge groups and the plethystic program

Abstract We present in the context of supersymmetric gauge theories an extension of the Weyl integration formula, first discovered by Robert Wendt [1], which applies to a class of non-connected Lie groups. This allows to count in a systematic way gauge-invariant chiral operators for these non-connected gauge groups. Applying this technique to O(n), we obtain, via the ADHM construction, the Hilbert series for certain instanton moduli spaces. We validate our general method and check our results via a Coulomb branch computation, using three-dimensional mirror symmetry

Wilson loop correlators at strong coupling in N=2\mathcal{N}=2 quiver gauge theories

We consider 4-dimensional $\mathcal{N} = 2$ superconformal quiver theories with $SU(N)^M$ gauge group and bi-fundamental matter and we evaluate correlation functions of $n$ coincident Wilson loops in the planar limit of the theory. Exploiting specific untwisted/twisted combinations of these operators and using supersymmetric localization, we are able to resum the whole perturbative expansion and find exact expressions for these correlators that are valid for all values of the 't Hooft coupling. Moreover, we analytically derive the leading strong coupling behaviour of the correlators, showing that they obey a remarkable simple rule. Our analysis is complemented by numerical checks based on a Pad\'e resummation of the perturbative series

Simulation of a Power Regulation System for Steam Power Plants

Abstract Renewable energy sources, presently constituting about 23% of the total Italian power production, are featured by very discontinuous supply during the day that, to avoid grid malfunctions, must be compensated by fossil fuelled power plants. The latter must hence be able to rapidly control power supply. This paper proposes a power regulation system for coal power plants, consisting in the bypass of the low pressure pre-heaters in order to increase the steam flow-rate in turbine. The main advantage of this system is the limited thermo-mechanical stress induced in the pre-heaters. The solution effectiveness is investigated through a Matlab-Simulink model