Integrated correlators in N = 4 SYM via SL(2, Z) spectral theory
Using supersymmetric localization and SL(2,Z) spectral theory we obtain exact results for a large class of integrated four-point functions of 1/2-BPS operators in N=4 SYM with gauge group SU(n). The integrated correlators we consider involve correlation functions of higher weight operators that are computable using the N=2* partition function deformed by higher weight couplings. These results, exact in the complexified gauge coupling, are governed by linear algebraic recursion relations which relate integrated correlators of different values of n and involving operators of different BPS charge. We find that the entire family of such correlators are completely fixed by these recursion formulas in terms of the integrated correlators of the 20' operators in the SU(2) theory. The SL(2,Z) spectral decomposition of these observables facilitate the large n expansion in the ’t Hooft limit and the very strongly coupled limit. Furthermore, the equivalence between ensemble averaging over the N=4 conformal manifold at large n and the strong ’t Hooft coupling limit allows us to compute new data for the regularized 1-loop AdS_5 x S^5 four-point scattering amplitudes involving external Kaluza-Klein states. We can also use our results to study the large BPS charge limit of a particularly simple subsector of these integrated correlation functions.