Calcolo di istantoni in teorie di gauge N=2 superconformi ​

The purpose of this work is to calculate the instanton corrections to the prepotential and the coupling constant in some N=2 superconformal gauge theories. We consider, at first, the N=2 SQCD, to which we also refer as A-theory, that contains 2N matter hypermultiplets in the fundamental representation of the gauge group; we explicitly evaluate the instanton prepotential with the SU(2) and SU(3) gauge group, in the massless case and in the massive one. Then, we examine the so-called N=2* theory, which consists of a massive adjoint hypermultiplet and it can be seen as a massive deformation of the N=4 SYM theory. Finally, we get to our main purpose and investigate the so-called E-theory, which is made up of one rank 2 symmetric hypermultiplet and one antisymmetric; we also study the theory with massive hypemultiplets, i.e. the E*-theory. After an introduction about supersymmetry and instantons, we properly describe the procedure to calculate the Nekrasov partition functions, from which we get the instanton corrections to the prepotential: the procedure is based on the equivariant cohomology and on the technique of supersymmetric localization. The non-perturbative series of the prepotential is calculated up to six instantons for SU(2) and up to four instantons for SU(3). For SQCD we obtain that the corrections to the coupling constant can be re-summed through the Jacobi theta functions, which was a known result, whereas for E-theory we get that the prepotential has no instanton corrections, just as N=4 SYM, and, in the massive case, the instanton corrections can be re-summed through the Eisenstein series. Both these results are new.