Universality of the operator product expansions of SCFT 4

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.