Abstract
We construct a family of 4d mathcal{N} = 1 theories that we call {E}_{rho}^{sigma } [USp(2N)] which exhibit a novel type of 4d IR duality very reminiscent of the mirror duality enjoyed by the 3d mathcal{N} = 4 {T}_{rho}^{sigma } [SU(N)] theories. We obtain the {E}_{rho}^{sigma } [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 } [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.
Highlights
We construct a family of 4d N = 1 theories that we call Eρσ[USp(2N )] which exhibit a novel type of 4d IR duality very reminiscent of the mirror duality enjoyed by the 3d N = 4 Tρσ[SU(N )] theories
The duality leaving the E[USp(2N )] theory invariant acts by exchanging operators charged under USp(2N )x with those charged under USp(2N )y much like the mirror selfduality for the 3d N = 4 T [SU(N )] theory exchanges the Higgs branch operators in the adjoint of the flavor SU(N ) group with the Coulomb branch operators in the adjoint of the other SU(N ) group emerging in the IR as an enhancement of the topological symmetries
In particular two of the E[USp(2N )] operators transforming under the USp(2N )x and USp(2N )y global symmetry and which are exchanged by the 4d duality reduce to the Coulomb and Higgs branch moment maps of T [SU(N )] which are swapped by Mirror Symmetry
Summary
We discuss the deformed duality web for E[USp(2N )] and we introduce the Eρσ[USp(2N )] theory with its mirror dual. Notice that these charges are consistent with the operator map dictated by Mirror Symmetry which in this case corresponds to a self-duality of the theory, under which the operators of the HB and the CB are exchanged.
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