The Exact Superconformal R-symmetry Minimizes $\tau_{RR}$

TL;DR

This paper introduces a new principle stating that the superconformal U(1)_R symmetry minimizes the two-point function coefficient τ_{RR}, providing a universal method to determine it in 4d and 3d SCFTs, with practical applications in AdS duals.

Contribution

The paper proposes τ_{RR} minimization as a new, general constraint for identifying superconformal U(1)_R symmetry in 4d and 3d SCFTs, offering an alternative to existing methods.

Findings

τ_{RR} minimization determines superconformal R-symmetry.

The method applies to both 4d and 3d SCFTs.

It is practically implementable in AdS dual geometries.

Abstract

We present a new, general constraint which, in principle, determines the superconformal $U(1)_R$ symmetry of 4d $\N =1$ SCFTs, and also 3d $\N =2$ SCFTs. Among all possibilities, the superconformal $U(1)_R$ is that which minimizes the coefficient, $\tau_{RR}$, of its two-point function. Equivalently, the superconformal $U(1)_R$ is the unique one with vanishing two-point function with every non-R flavor symmetry. For 4d $\N =1$ SCFTs, $\tau_{RR}$ minimization gives an alternative to a-maximization. $\tau_{RR}$ minimization also applies in 3d, where no condition for determining the superconformal $U(1)_R$ had been previously known. Unfortunately, this constraint seems impractical to implement for interacting field theories. But it can be readily implemented in the AdS geometry for SCFTs with AdS duals.