From Chern-Simons to Tomonaga-Luttinger
arXiv:1712.08744 · doi:10.1142/S0217751X18500136
Abstract
A single-sided boundary is introduced in the three-dimensional Chern-Simons model. It is shown that only one boundary condition for the gauge fields is possible, which plays the twofold role of chirality condition and bosonization rule for the two-dimensional Weyl fermion describing the degrees of freedom of the edge states of the Fractional Quantum Hall Effect. It is derived the symmetry on the boundary which determines the effective two dimensional action, whose equation of motion coincides with the continuity equation of the Tomonaga-Luttinger theory. The role of Lorentz symmetry and of discrete symmetries on the boundary is also discussed.
arXiv comment14 pages
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- Quasi-topological fractons: a 3D dipolar gauge theory
- Edge physics and the Casimir interaction in Maxwell-Chern-Simons theory on a strip
- Notes from the bulk: metric dependence of the edge states of Chern-Simons theory