Lattice Construction of Duality with Non-Abelian Gauge Fields in 2+1D
arXiv:1806.04155 · doi:10.1103/PhysRevB.100.075109
Abstract
The lattice construction of Euclidean path integrals has been a successful approach of deriving 2+1D field theory dualities with a U gauge field. In this work, we generalize this lattice construction to dualities with non-Abelian gauge fields. We construct the Euclidean spacetime lattice path integral for a theory with strongly-interacting vector bosons and Majorana fermions coupled to an gauge field and derive an exact duality between this theory and the theory of a free Majorana fermion on the spacetime lattice. We argue that this lattice duality implies the desired infrared duality between the field theory with an vector critical boson coupled to an Chern-Simons gauge theory, and a free massless Majorana fermion in 2+1D. We also generalize the lattice construction of dualities to models with gauge fields.
arXiv comment7 pages+Appendix
References in corpus (44)
- A Duality Web in 2+1 Dimensions and Condensed Matter Physics
- Chern-Simons Theory with Vector Fermion Matter
- Is the Composite Fermion a Dirac Particle?
- Deconfined quantum critical points: symmetries and dualities
- Level/rank Duality and Chern-Simons-Matter Theories
- d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
- Particle-Vortex Duality from 3d Bosonization
- Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
- Baryons, monopoles and dualities in Chern-Simons-matter theories
- Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
- Time-Reversal Breaking in QCD, Walls, and Dualities in 2+1 Dimensions
- Dual Dirac liquid on the surface of the electron topological insulator
- Chern-Simons Currents and Chiral Fermions on the Lattice
- The Thermal Free Energy in Large N Chern-Simons-Matter Theories
- Chern-Simons-matter dualities with and gauge groups
- Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
- Mott Transition in An Anyon Gas
- Chern Simons duality with a fundamental boson and fermion
- Duality between the deconfined quantum-critical point and the bosonic topological transition
- Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
- Phases Of Adjoint QCD And Dualities
- Bosonization and Mirror Symmetry
- Nonsupersymmetric dualities from mirror symmetry
- Self-dual Quantum Electrodynamics as Boundary State of the three dimensional Bosonic Topological Insulator
- More Abelian Dualities in 2+1 Dimensions
- Composite fermi liquids in the lowest Landau level
- Three-dimensional dualities with bosons and fermions
- Modular Invariance, Self-Duality and The Phase Transition Between Quantum Hall Plateaus
- Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)
- Duality and bosonization of (2+1)d Majorana fermions
- Exact Boson-Fermion Duality on a 3D Euclidean Lattice
- Symmetry and duality in bosonization of two-dimensional Dirac fermions
- Composite fermion duality for half-filled multicomponent Landau Levels
- Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
- Non-Abelian 3d Bosonization and Quantum Hall States
- A master bosonization duality
- Bosonizing three-dimensional quiver gauge theories
- Flavor and topological current correlators in parity-invariant three-dimensional QED
- A series of (2+1)d Stable Self-Dual Interacting Conformal Field Theories
- Loop Models, Modular Invariance, and Three Dimensional Bosonization
- Strong-Weak Chern-Simons-Matter Dualities from a Lattice Construction
- Mirror Symmetry and Bosonization in 2d and 3d
- Chern-Simons theory coupled to bifundamental scalars
- Non-Abelian Fermionization and Fractional Quantum Hall Transitions