Exploring the 4d Superconformal Zoo

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 &#34;a-theorem&#34; for N=1 SCFTs. Using this &#34;a-maximization&#34;, 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&#39;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 &#34;a-theorem&#34; conjecture, a_{IR}<a_{UV}, in every case