Exploring the 4d Superconformal Zoo

TL;DR

This paper introduces a method called a-maximization to precisely determine the superconformal R-symmetry in 4d N=1 SCFTs, enabling exact results and classification of these theories, and supporting the a-theorem conjecture.

Contribution

It presents a-maximization as a new constraint for identifying superconformal R-symmetry, connecting ADE singularities to SCFT classification, and verifying the a-theorem in various cases.

Findings

Successfully classified a wide range of SCFTs using ADE singularity types.

Confirmed all RG flows satisfy the a-theorem, with IR a-values less than UV a-values.

Provided exact results for previously inaccessible 4d N=1 SCFTs.

Abstract

We discuss a new constraint for determining the superconformal U(1)_R symmetry of 4d N=1 SCFTs: It is the unique one which locally maximizes a(R) = 3Tr R^3-Tr R. This constraint comes close to proving the conjectured "a-theorem" for N=1 SCFTs. Using this "a-maximization", exact results can now be obtained for previously inaccessible 4d N=1 SCFTs. We apply this method to a rich class of examples: 4d N=1 SQCD with added matter chiral superfields in the adjoint representation. We classify a zoo of SCFTs, finding that Arnold's ADE singularity classification arises in classifying these theories via all possible relevant Landau-Ginzburg superpotentials. We verify that all RG flows are indeed compatible with the "a-theorem" conjecture, a_{IR}<a_{UV}, in every case