Non-abelian bosonization in two and three spatial dimensions and applications

Abstract

In this paper, we generalize Witten's non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. We apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$-flux phase, critical spin liquids in 1,2,3 spatial dimensions, and twisted bilayer graphene.

arXiv commentv2: Slight revision of the twisted-bilayer graphene section. New references added

References in corpus (30)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Moire bands in twisted double-layer graphene
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Tuning superconductivity in twisted bilayer graphene
• Periodic table for topological insulators and superconductors
• Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
• Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
• Intrinsic quantized anomalous Hall effect in a moiré heterostructure
• "Deconfined" quantum critical points
• The effects of interactions on the topological classification of free fermion systems
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Cascade of electronic transitions in magic-angle twisted bilayer graphene
• Cascade of Phase Transitions and Dirac Revivals in Magic Angle Graphene
• Deconfined quantum critical points: symmetries and dualities
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Competing orders, non-linear sigma models, and topological terms in quantum magnets
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Reflection positivity and invertible topological phases
• Theta-terms in nonlinear sigma-models
• Dual Dirac liquid on the surface of the electron topological insulator
• Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• Superconductivity, correlated insulators, and Wess-Zumino-Witten terms in twisted bilayer graphene
• Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
• A square lattice algebraic spin liquid with SO(5) symmetry
• Hopf term induced by fermions
• A Holographic Theory for the Phase Transitions Between Fermionic Symmetry-protected Topological States
• The "non-regularizability" of gapless free fermion Hamiltonian protected by on-site symmetries

Cited by in corpus (6)

• Competing orders, the Wess-Zumino-Witten term, and spin liquids
• Phase transitions on the dark side of the Gross-Neveu model: Spontaneous $\text{O}(4N)$ symmetry breaking at repulsive coupling
• Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions
• The electromagnetic duality and the 3+1D O(6) non-linear sigma model with a level-1 Wess-Zumino-Witten term
• Current Algebra Approach to 2d Chiral Metals
• Separation of quadrupole, spin, and charge across the magnetic phases of a one-dimensional interacting spin-1 gas