Abstract
We study the conformal bootstrap constraints for 4D $\mathcal{N}=1$ superconformal field theories containing a chiral operator $\phi$ and the chiral ring relation $\phi^2=0$. Hints for a minimal interacting SCFT in this class have appeared in previous numerical bootstrap studies. We perform a detailed study of the properties of this conjectured theory, establishing that the corresponding solution to the bootstrap constraints contains a $\text{U}(1)_R$ current multiplet and estimating the central charge and low-lying operator spectrum of this theory.
Highlights
Upper bounds merge at the minimal value of ∆φ
We study the conformal bootstrap constraints for 4D N = 1 superconformal field theories containing a chiral operator φ and the chiral ring relation φ2 = 0
We perform a detailed study of the properties of this conjectured theory, establishing that the corresponding solution to the bootstrap constraints contains a U(1)R current multiplet and estimating the central charge and low-lying operator spectrum of this theory
Summary
We perform a detailed study of the properties of this conjectured theory, establishing that the corresponding solution to the bootstrap constraints contains a U(1)R current multiplet and estimating the central charge and low-lying operator spectrum of this theory. We estimate that this minimal theory has c/cfree 8/3 where cfree is the central charge of a free chiral multiplet.
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