A Critical Behaviour of Anomalous Currents, Electric-Magnetic Universality and CFT_4

TL;DR

This paper explores anomalous currents, duality, and conformal properties in four-dimensional superconformal field theories, revealing new relations between anomalous dimensions, beta function slopes, and operator mixing near critical points.

Contribution

It extends electric-magnetic duality to nonchiral currents and computes the beta function slope at strong coupling in 4D SCFTs, highlighting operator mixing and duality near fixed points.

Findings

Anomalous dimension of Konishi current relates to beta function slope.

Operator $ ext{Sigma}$ mixes with stress tensor OPE, affecting conformal structure.

Duality extends to a neighborhood of the critical point, with two central charges c and c'.

Abstract

We discuss several aspects of superconformal field theories in four dimensions (CFT_4), in the context of electric-magnetic duality. We analyse the behaviour of anomalous currents under RG flow to a conformal fixed point in N=1, D=4 supersymmetric gauge theories. We prove that the anomalous dimension of the Konishi current is related to the slope of the beta function at the critical point. We extend the duality map to the (nonchiral) Konishi current. As a byproduct we compute the slope of the beta function in the strong coupling regime. We note that the OPE of $T_{\mu\nu}$ 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 SCFT_4 seems to be naturally equipped with a privileged off-critical deformation $\Sigma$ and this allows us to argue that electric-magnetic duality can be extended to a neighborhood of the critical point. We also stress that in SCFT_4 there are two central charges, c and c', associated with the stress tensor and $\Sigma$, respectively; c and c' allow us to count both the vector multiplet and the matter multiplet effective degrees of freedom of the theory.