In this talk, we bootstrap various objects in planar maximally supersymmetric Yang- Mills theory. Focusing on the four-point correlation function of stress-tensor, we first demonstrate why the conventional bootstrap approach fails and new techniques are required. Next, we introduce a set of sum rules that are tailored for this problem as they are sensitive only to single-traces in the OPE expansion. Integrability enters at this stage and provides information on the spectrum of these operators. Their OPE coefficients, however, remain elusive. We then discuss how these sum rules can be employed in numerical bootstrap to nonperturbatively bound the OPE coefficients, the four-point correlation function and the energy-energy correlator. We show, for the first time, rigorous non-perturbative results for the planar OPE coefficient of single-trace operators as well as the correlation function at various points in cross-ratio space. Additionally, focusing on the energy-energy correlator (EEC), we present rigorous bounds for its spin 2 and spin 3 Legendre coefficients as well as the full EEC function at various angles. These results were obtained for a wide range of t’Hooft couplings, highlighting the power of the bootstrap in probing non-perturbative aspects of planar N=4 SYM theory.
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Julio Parra-Martinez
