| Summary: | Abstract We suggest three new N $$ \mathcal{N} $$ = 1 conformal dual pairs. First, we argue that the N $$ \mathcal{N} $$ = 2 E 6 Minahan-Nemeschansky (MN) theory with a USp(4) subgroup of the E 6 global symmetry conformally gauged with an N $$ \mathcal{N} $$ = 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 $$ \mathcal{N} $$ = 2 E 7 MN theory with an SU(2) subgroup of the E 7 global symmetry conformally gauged with an N $$ \mathcal{N} $$ = 1 vector multiplet and certain additional chiral multiplet matter resides at some cusp of the conformal manifold of a conformal N $$ \mathcal{N} $$ = 1 USp(4) gauge theory. Finally, we claim that the N $$ \mathcal{N} $$ = 2 E 8 MN theory with a USp(4) subgroup of the E 8 global symmetry conformally gauged with an N $$ \mathcal{N} $$ = 1 vector multiplet and certain additional chiral multiplet matter resides at some cusp of the conformal manifold of an N $$ \mathcal{N} $$ = 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 $$ \mathcal{N} $$ = 1 analogues of N $$ \mathcal{N} $$ = 2 Argyres-Seiberg/Argyres-Wittig duals of the E n MN models. We also briefly comment on an N $$ \mathcal{N} $$ = 1 version of the Schur limit of the superconformal index.
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