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In this talk I will discuss a non-lagrangian non-perturbative approach to 4D CFTs. After giving all the necessary definitions I will present a general form of arbitrary spin n-point functions required by the conformal symmetry. I will then use the OPE to investigate further and compute explicitly arbitrary spin 4-point functions. The discussion will be facilitated with concrete examples. I will conclude with applications of these results for constraining the parameter space of 4D CFTs (conformal bootstrap).
