A matrix model approach to integrated correlators in N=2 Super Yang-Mills theories

The goal of the thesis is the computation of the integrated correlator of four moment-map operators in the large N limit, using supersymmetric localization, in the N=4 SYM theory with gauge group SU(N) and in a particular superconformal N=2 SYM theory, the E-theory, with matter hypermultiplets transforming in the symmetric and in the antisymmetric representation of SU(N). Localization allows to obtain exact results, valid for all values of the coupling, for the planar and subplanar terms and from these it is possible to extract the asymptotic expansion at strong coupling. Comparing the results obtained for the two theories, it turns out that the planar terms of the two integrated correlators are equal, despite the reduced amount of supersymmetry of the E-theory, while the difference between the two theories appear in the subplanar terms. ​