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Duality Between 3D Massive Thirring and Maxwell-Chern-Simons Models from 2D Bosonization.

Carlos A Hernaski¹, Pedro R S Gomes¹

¹Departamento de Física, Universidade Estadual de Londrina, Caixa Postal 10011, 86057-970, Londrina, Paraná, Brazil.

Physical Review Letters

|August 11, 2018

Summary

We demonstrate how fermion-boson mapping in three dimensions arises from two-dimensional bosonization. This reveals connections between quantum field theory models and topological order.

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Area of Science:

Quantum Field Theory
Condensed Matter Physics

Background:

Bosonization techniques are crucial nonperturbative tools in quantum field theory.
In three dimensions, these techniques connect to topologically ordered systems and dualities.

Purpose of the Study:

To derive the fermion-boson mapping between the massive Thirring model and the Maxwell-Chern-Simons model in three dimensions.
To show this mapping originates from exact bosonization in two dimensions.

Main Methods:

Utilizing the quantum wires formalism.
Applying exact bosonization techniques from two dimensions.

Main Results:

The study successfully derives the fermion-boson mapping for the low-energy regime of the massive Thirring model.
This derivation demonstrates a link between the three-dimensional Thirring model and the Maxwell-Chern-Simons model.

Conclusions:

The quantum wires formalism provides a pathway to understand complex mappings in quantum field theory.
This work bridges concepts from two-dimensional bosonization to three-dimensional topological systems.