4d mirror-like dualities

We construct a family of 4d$$ \mathcal{N} $$ N = 1 theories that we call $$ {E}_{\rho}^{\sigma } $$ E ρ σ [USp(2N)] which exhibit a novel type of 4d IR duality very reminiscent of the mirror duality enjoyed by the 3d$$ \mathcal{N} $$ N = 4 $$ {T}_{\rho}^{\sigma } $$ T ρ σ [SU(N)] theories. We obtain the $$ {E}_{\rho}^{\sigma } $$ E ρ σ [USp(2N)] theories from the recently introduced E[USp(2N )] theory, by following the RG flow initiated by vevs labelled by partitions ρ and σ for two operators transforming in the antisymmetric representations of the USp(2N) × USp(2N) IR symmetries of the E[USp(2N)] theory. These vevs are the 4d uplift of the ones we turn on for the moment maps of T[SU(N)] to trigger the flow to $$ {T}_{\rho}^{\sigma } $$ T ρ σ [SU(N)]. Indeed the E[USp(2N)] theory, upon dimensional reduction and suitable real mass deformations, reduces to the T[SU(N)] theory. In order to study the RG flows triggered by the vevs we develop a new strategy based on the duality webs of the T[SU(N)] and E[USp(2N)] theories.