Landscape of Simple Superconformal Field Theories in 4d

Kazunobu Maruyoshi, Emily Nardoni, Jaewon Song

Published 2018-06-21Version 1

We explore the infrared fixed points of four-dimensional $\mathcal{N}=1$ supersymmetric $SU(2)$ gauge theory coupled to an adjoint and two fundamental chiral multiplets under all possible relevant deformations and F-term couplings to gauge-singlet chiral multiplets. We find 35 fixed points, including the $\mathcal{N}=2$ Argyres-Douglas theories $H_0$ and $H_1$. The theory with minimal central charge $a$ is identical to the mass-deformed $H_0$ theory, and the one with minimal $c$ has the smallest $a$ among the theories with $U(1)$ flavor symmetry. We also find a "next to minimal" $\mathcal{N}=1$ SCFT with a chiral operator $\mathcal{O}$ with relation $\mathcal{O}^3 = 0$. In addition, we find 30 candidate fixed point theories possessing unphysical operators--including one with $(a, c) \simeq (0.20, 0.22)$--that need further investigation.