N = 1 conformal duals of gauged E_n MN models

We suggest three new N = 1 conformal dual pairs. First, we argue that the N = 2 E₆ Minahan-Nemeschansky (MN) theory with a USp(4) subgroup of the E₆ global symmetry conformally gauged with an N = 1 vector multiplet and certain additional chiral multiplet matter resides at some cusp of the conformal manifold of an SU(2)⁵ quiver gauge theory. Second, we argue that the N = 2 E₇ MN theory with an SU(2) subgroup of the E₇ global symmetry conformally gauged with an N = 1 vector multiplet and certain additional chiral multiplet matter resides at some cusp of the conformal manifold of a conformal N = 1 USp(4) gauge theory. Finally, we claim that the N = 2 E₈ MN theory with a USp(4) subgroup of the E₈ global symmetry conformally gauged with an N = 1 vector multiplet and certain additional chiral multiplet matter resides at some cusp of the conformal manifold of an N = 1 Spin(7) conformal gauge theory. We argue for the dualities using a variety of non-perturbative techniques including anomaly and index computations. The dualities can be viewed as N = 1 analogues of N = 2 Argyres-Seiberg/Argyres-Wittig duals of the E_n MN models. We also briefly comment on an N = 1 version of the Schur limit of the superconformal index.