4d mirror-like dualities

Abstract

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.

New 2d $$ \mathcal{N} $$ = (0, 2) dualities from four dimensions

“…It also corresponds to the self-duality of the E[U Sp (4)] theory of [45] (see also [46,47] for other interesting IR properties of this theory). 20 As it was already pointed out in [17], this theory is asymptotically free only for N < 4, so the 4d duality that we are considering becomes a duality between IR free theories if N is too large. Nevertheless, it may still happen that upon compactification it reduces to a duality between interacting theories also for N > 4.…”

“…In [49] it was shown how to derive this duality for arbitrary N by applying piecewise the duality for N = 1, which relates the U (1) gauge theory with one fundamental flavor to a free hypermultiplet (see also [50] for an implementation of this procedure at the level of the three-sphere partition function and [51] for the N = 2 case). The four-dimensional duality of which we are considering the 2d reduction is an higher dimensional ancestor of this mirror duality and in [17] it was shown that a similar piecewise derivation applies also in 4d, where the fundamental duality that should be iterated is the Seiberg duality of SU (2) with 6 chirals dual to a WZ model of 15 chirals.…”

“…In section 3 we propose a new 2d duality for a U Sp(2N ) gauge theory with antisymmetric matter, which is obtained from a parent four-dimensional duality discussed in [16]. In section 4 we propose an infinite dimensional family of dual frames made of SU (2) linear quiver gauge theories of arbitrary length N − 1 and with N Fermi singlets, where N is a non-negative integer number, which is derived from one of the 4d mirror-like dualities of [17]. In appendix A we comment on the possibility of another duality for a U Sp(2N ) gauge theory with antisymmetric matter, but with a different number of fundamental matter fields than the one of section 3.…”

“…This three-dimensional duality relates a U (N ) gauge theory with one adjoint chiral A, one fundamental flavor Q and N chiral singlets with superpotential 16 Also this duality can be derived by iterative applications of some more fundamental confining dualities, as it was shown in [39] at the level of the S 3 b partition function. 17 Such more fundamental dualities correspond to the confining cases of Aharony duality [42] and a variant with monopole superpotential [43], which can also be derived as limits of the compactification of the 4d Intriligator-Pouliot JHEP12(2020)009 duality. Hence, the 2d duality we are proposing and its derivation complete this picture: we have an analogue of the same duality in 2d, 3d and 4d, as well as an analogue of their derivation by iteration of confining dualities.…”

“…The four-dimensional duality we want to consider is one of the recently proposed 4d mirrorlike dualities [17]. More precisely, following the same nomenclature of [ 19 This duality can be considered as a four-dimensional uplift of the 3d N = 4 abelian mirror duality that relates a U (1) gauge theory with N flavors of fundamental hypermultiplets and a linear abelian quiver with N − 1 U (1) gauge nodes and one flavor attached to each end of the tail [48].…”