Anomalous Currents in SCFT$_4$

TL;DR

This paper investigates anomalous currents in 4D N=1 superconformal gauge theories, relating their anomalous dimensions to beta function slopes, constructing duality maps, and exploring implications for central charges and N=4 SYM.

Contribution

It establishes a relation between anomalous current dimensions and beta function slopes, constructs a duality map for the Konishi current, and analyzes the mixing of stress tensor OPEs in SCFT$_4$.

Findings

The anomalous dimension of the Konishi superfield is linked to the beta function slope.

A duality map for the Konishi current in minimal SQCD is constructed.

The OPE of the stress tensor with itself mixes with the Konishi operator, revealing two central charges.

Abstract

We analyse the critical behaviour of anomalous currents in N=1 four-dimensional supersymmetric gauge theories in the context of electric-magnetic duality. We show that the anomalous dimension of the Konishi superfield is related to the slope of the beta function at the critical point. We construct a duality map for the Konishi current in the minimal SQCD. As a byproduct we compute the slope of the beta function in the strong coupling regime. We note that the OPE of the stress tensor with itself does not close, but mixes with the Konishi operator. As a result in superconformal theories in four dimensions (SCFT$_4$) there are {\sl two} central charges; they allow us to count both the vector multiplet and the matter multiplet effective degrees of freedom. Some applications to N=4 SYM are discussed.