More N=4 superconformal bootstrap

In this long overdue second installment, we continue to develop the conformal bootstrap program for N=4 superconformal field theories (SCFTs) in four dimensions via an analysis of the correlation function of four stress-tensor supermultiplets. We review analytic results for this correlator and make contact with the SCFT/chiral algebra correspondence of Beem et al. [Commun. Math. Phys. 336, 1359 (2015)CMPHAY0010-361610.1007/s00220-014-2272-x]. We demonstrate that the constraints of unitarity and crossing symmetry require the central charge c to be greater than or equal to 3/4 in any interacting N=4 SCFT. We apply numerical bootstrap methods to derive upper bounds on scaling dimensions and operator product expansion coefficients for several low-lying, unprotected operators as a function of the central charge. We interpret our bounds in the context of N=4 super Yang-Mills theories, formulating a series of conjectures regarding the embedding of the conformal manifold- parametrized by the complexified gauge coupling- into the space of scaling dimensions and operator product expansion coefficients. Our conjectures assign a distinguished role to points on the conformal manifold that are self-dual under a subgroup of the S-duality group. This paper contains a more detailed exposition of a number of results previously reported in Beem et al. [Phys. Rev. Lett. 111, 071601 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.071601] in addition to new results.