Non-abelian 3D bosonization and quantum Hall states

Abstract

Bosonization dualities relate two different Chern-Simons-matter theories, with bosonic matter on one side replaced by fermionic matter on the other. We first describe a more general class of non-Abelian bosonization dualities. We then explore the nonrelativistic physics of these theories in the quantum Hall regime. The bosonic theory lies in a condensed phase and admits vortices which are known to form a non-Abelian quantum Hall state. We ask how this same physics arises in the fermionic theory. We find that a condensed boson corresponds to a fully filled Landau level of fermions, while bosonic vortices map to fermionic holes. We confirm that the ground state of the two theories is indeed described by the same quantum Hall wavefunction.

A symmetry breaking scenario for QCD3

“…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

“…The same procedure with a slightly different choice of background U(1) Chern-Simons level on both sides gives the U/U duality. A completely general choice of U(1) Chern-Simons level leads to yet more dualities between U(N ) theories and U(k) × U(1) theories where the U(1) factor is topological [40].…”

Monopole operators in U(1) Chern-Simons-matter theories

“…Understanding the properties of monopole operators is important for characterizing the universality classes of these second order phase transitions. Another motivation comes from the recently discussed web of nonsuperymmetric dualities [37][38][39][40][41][42][43][44][45][46][47][48][49][50]. Under the duality map, monopole operators sometimes get mapped to operators built from the elementary fields of the dual theory.…”