Universality of the operator product expansions of SCFT4

Abstract We study the operator product algebra of the supercurrent J α α and Konishi superfield K in four-dimensional supersymmetric gauge theories. The Konishi superfield appears in the JJ OPE and the algebra is characterized by two central charges c and c ′ and an anomalous dimension h for K . In free field (one-loop) approximation, c ∼ 3 N ν + N χ and c ′ ∼ N χ , where N ν and N χ are, respectively, the number of vector and chiral multiplets in the theory. In higher order c , c ′ and h depend on the gauge and Yukawa couplings and we obtain the two-loop contributions by combining earlier work on c with our own calculations of c ′ and h . The major result is that the radiative corrections to the central charges cancel when the one-loop beta-functions vanish, suggesting that c and c ′ are invariant under continuous deformations of superconformal theories. The behavior of c and c ′ along renormalization group flows is studied from the viewpoint of a c -theorem.