Universality of the Operator Product Expansions of SCFT_4

TL;DR

This paper investigates the operator product expansions in 4D superconformal field theories, revealing that certain central charges remain invariant under specific conditions, and explores their behavior along renormalization group flows.

Contribution

It provides a detailed analysis of the operator algebra involving the supercurrent and Konishi superfield, including two-loop corrections and invariance properties of central charges.

Findings

Radiative corrections to central charges cancel at vanishing one-loop beta-functions.

c and c' are invariant under continuous deformations when beta-functions vanish.

The study offers insights into the behavior of central charges along RG flows in superconformal theories.

Abstract

We study the operator product algebra of the supercurrent J 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~3N_v+N_\chi and c'~N_\chi, where N_v and N_\chi 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'. 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' (but not h) 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.