New and old fermionic dualities from 3d bosonization

Abstract

We construct novel fermion-fermion dualities in 2+1-dimensions using 3d bosonization dualities. This is achieved by relating two-node quiver theories using both the flavorbounded and flavor-violated 3d bosonization dualities. Such quivers can be viewed as a generalization of the fermionic particle-vortex duality. A special case of these quivers exhibits a Z 2 symmetry under interchange of the two nodes. Using orbifold techniques, we show that such dualities provide a novel way of deriving known 3d bosonization dualities with adjoint matter, thus unifying the non-Abelian bosonization dualities in an even larger duality web. We then use this construction to derive new dualities involving adjoint matter.

Phases of two adjoints QCD3 and a duality chain

“…with adjoint/rank-two fermions. This difference has already appeared in the case of single bifundamental versus single adjoint/rank-two QCD 3 as discussed in [58]. Namely, the quantum phase of the bifundamental theory admits a scalar dual description with a bifundamental representation.…”

“…Story is very similar to the general pair of rank-two/adjoint fermions so far treated above. When there is a single bifundamental fermion, 'weakly coupled' dual descriptions are exist which shares the same intermediate phase by level/rank duality [58]. In the presence of two bifundamental fermions, direct description of phase transition in terms of weakly coupled theory is not manageable, and it is also natural to conjecture that similar duality chain would give the information about the quantum phase.…”

“…), it is also natural to ask whether we could connect the two bifundamental theories to the theory of two adjoint fermions. The answer was positive for the case of single bifundamental and single adjoint fermions in [58] using the orbifold projection. Similar technique gives a positive answer between two bifundamentals and two adjoints by using similar Z 2 automorphisms along the dualities to single flavor case.…”

“…Now the bosonization is carried out at the two distinguished critical points with two different mutually non-local dual descriptions [3]. This shape of the phase diagram has been successfully applied to the case of single adjoint/rank-two matter and some other cases such as single bifundamental fermions [4,5,[7][8][9]58] with various supporting checks [59][60][61][62][63][64][65]. (See [66] for the recent lecture note covering many aspects discussed above.)…”

“…One is the dynamics of QCD 3 with arbitrary pair of fermions in the adjoint/rank-two representations which is the full generalization of the QCD 3 with single flavor fermion in adjoint/rank-two representation [4,7]. The other is the dynamics of the 2-node quiver gauge theory with two bifundamental fermions which is the generalization of the QCD 3 with the vector fermions [3] by gauging flavor symmetry [58]. It is important to note that the latter model with two bifundamental fermions passes more stringent consistency checks due to its distinguished characteristics and we propose possible 2+1d orbifold equivalence [58,67] between two theories at the end of this paper.…”