More Abelian dualities in 2 + 1 dimensions

Abstract

Abstract:We expand on the recent derivation of 3d dualities using bosonization. We present in some detail a general class of Abelian duals.

A master bosonization duality

“…These dualities have been the subject of recent attention from a variety of viewpoints. For the special case N = k = N f = 1, these dualities are related to the surface states of time-reversal invariant topological insulators and the fractional quantum Hall effect at half filling [10][11][12][13], lead to a web of dualities [14][15][16][17], and can even be proven on the lattice [18]. They are crucial actors in mapping out the phase diagram of QCD 3 as well as some of its cousins.…”

“…The first is that this proposal reduces to Aharony's when N s = 0 or N f = 0. The second concerns recent works which use the basic dualities as "seed dualities" to generate new ones by gauging global symmetries on both sides of the seed [14][15][16][17]22]. In the context of quiver gauge theories, one of the results of [22] is that one can dualize node-by-node: given a quiver with a SU or U gauge group factor coupled to only bosons or fermions, one can generate a dual quiver by replacing a node and the matter attached to it with its dual according to (1.2) and (1.3).…”

“…In the Higgs phase we have SU(N ) → 0, and the only remnant of the scalars is a single compact Goldstone boson. Dualizing it into pure electromagnetism, we write the various phases as 17) and Phase III splits into Phases IIIa and IIIb depending on whether the fermions (note that since the gauge group is trivial in the Higgs phase all fermions are "singlets.") get a negative or positive mass.…”

Three-dimensional topological insulators and bosonization

“…Recently, several authors have suggested that flux attachment also holds for relativistic theories [74][75][76][77][78][79][80]. For example, a map exists between the Dirac fermion and complex scalar theories, both including self-interactions, with the boson coupled to the Chern-Simons field for changing statistics [79,80].…”

“…For example, a map exists between the Dirac fermion and complex scalar theories, both including self-interactions, with the boson coupled to the Chern-Simons field for changing statistics [79,80]. In our analysis of the bosonic theory, we do not include the Chern-Simons field, but the flux attachment is represented by the choice of boundary conditions for the soliton excitations in the Ramond sector (3.50)-(3.51), corresponding to half fluxes added along the two spatial cycles of the torus.…”