A CRITICAL-BEHAVIOR OF ANOMALOUS CURRENTS, ELECTRIC-MAGNETIC UNIVERSALITY AND CFT4

We discuss several aspects of superconformal field theories in four di mensions (CFT4), in the context of electric-magnetic duality, We analy se the behaviour of anomalous currents under RG flow to a conformal fi xed point in N = 1, D = 4 supersymmetric gauge theories. We prove that the anomalous dimension of the Konishi current is related to the slop e of the beta function at the critical point. We extend the duality ma p to the (nonchiral) Konishi current. As a byproduct we compute the sl ope of the beta function in the strong coupling regime. We note that t he OPE of T-mu v with itself does not close, but mixes with a special additional operator Sigma which in general is the Konishi current. We discuss the implications of this fact in generic interacting conformal theories. In particular, a SCFT4 seems to be naturally equipped with a privileged off-critical deformation Sigma and this allows us to argu e that electric-magnetic duality can be extended to a neighbourhood of the critical point We also stress that in SCFT4 there are two central charges, c and c', associated with the stress tensor and Sigma, respe ctively; c and c' allow us to count both the vector multiplet and the matter multiplet effective degrees of freedom of the theory. (C) 1997 Elsevier Science B.V.