Four-point functions in N = 4 SYM

Abstract

A new derivation is given of four-point functions of charge Q chiral primary multiplets in N = 4 supersymmetric Yang-Mills theory. A compact formula, valid for arbitrary Q, is given which is manifestly superconformal and analytic in the internal bosonic coordinates of analytic superspace. This formula allows one to determine the spacetime four-point function of any four component fields in the multiplets in terms of the four-point function of the leading chiral primary fields. The leading term is expressed in terms of 1/2Q(Q - 1) functions of two conformal invariants and a number of single variable functions. Crossing symmetry reduces the number of independent functions, while the OPE implies that the single-variable functions arise from protected operators and should therefore take their free form. This is the partial non-renormalisation property of such four-point functions which can be viewed as a consequence of the OPE and the nonrenormalisation of three-point functions of protected operators. © SISSA/ISAS 2003.