Particle-vortex duality in topological insulators and superconductors

Abstract

Abstract:We investigate the origins and implications of the duality between topological insulators and topological superconductors in three and four spacetime dimensions. In the latter, the duality transformation can be made at the level of the path integral in the standard way, while in three dimensions, it takes the form of "self-duality in odd dimensions". In this sense, it is closely related to the particle-vortex duality of planar systems. In particular, we use this to elaborate on Son's conjecture that a three dimensional Dirac fermion that can be thought of as the surface mode of a four dimensional topological insulator is dual to a composite fermion.

A symmetry breaking scenario for QCD3

“…The resulting space is not simply connected π 1 (Ṽ) = Z 2 . 12 We see that the underlying Z 2 one-from global symmetry, which is associated with the center of Spin(N ), is realized as a one-form global symmetry in the macroscopic theory. Because of this nontrivial π 1 the macroscopic theory has stable Z 2 strings.…”

“…The dynamics of 2+1 dimensional non-Abelian gauge theories has been recently revitalised by the proposal of boson/fermion dualities [2][3][4][10][11][12][13][14][15][16][17][18]. They were motivated by ideas in 2 + 1d field theory [19][20][21][22][23][24], supersymmetric quantum field theory [9,[25][26][27][28][29][30][31][32][33][34][35][36], and string theory [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51].…”

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).…”

Scaling dimensions in QED3 from the ϵ-expansion

“…Namely, refs. [33][34][35] argued, based on 3d bosonization dualities [36][37][38][39], that for N f = 1 the SU(2) × U(1) symmetry is in fact enhanced to O(4) (this is related to the self-duality present in this theory [40]). Also, a recent lattice study [41] found no evidence for a symmetry-breaking condensate (for previous lattice studies see refs.…”