By Patrick Allen
Harnessing SL(2, Z) in Super Yang–Mills and Gravity
We introduce a new approach to extracting the physical consequences of S-duality for observables of four-dimensional N=4 super Yang-Mills (SYM) theory. The main mathematical tool is the theory of harmonic analysis on the fundamental domain of SL(2,Z). Applying this technology leads to strong constraints on the analytic structure of observables in N=4 SYM. We treat a specific set of integrated correlators in some detail, which simplify drastically when expressed in the SL(2,Z)-invariant eigenbasis. We initiate the study of the statistics of CFT data in the ensemble of N=4 SYM theories. At large N, this has ramifications for holography. In a sense to be made precise, we show an equivalence between observables in the strongly coupled planar theory, dual to type IIB supergravity on AdS5 x S5, and their ensemble average over the N=4 SYM conformal manifold.