Abstract
Bosonization techniques are important nonperturbative tools in quantum field theory. In three dimensions they possess interesting connections to topologically ordered systems and ultimately have driven the observation of an impressive web of dualities. In this work, we use the quantum wires formalism to show how the fermion-boson mapping relating the low-energy regime of the massive Thirring model in three spacetime dimensions with the Maxwell-Chern-Simons model can be obtained from the exact bosonization in two dimensions.
Highlights
Introduction.—Bosonization is one of the main tools to analyze nonperturbative properties of quantum field theories and condensed matter systems in 1 þ 1 dimensions (2D)
The authors in Ref. [11] showed the relation between the massive Thirring model (TM) in 3D with the Maxwell-Chern-Simons (MCS) model in the large mass limit
The emergence of a gauge invariance from the TM comes as a surprise in the approach of Ref. [11]
Summary
To track back the local charge dynamics in the quantum wires system, we need to investigate the flow of charge into and out of each wire due to charge tunneling interaction operators, i.e., the operators that break the Uð1Þ symmetry ψi0 1⁄4 eiαi ψi, which corresponds to an independent global transformation for each one of the wires. Pursuing this analysis, one obtains the expression of the intrawire charge nonconservation ∂tJit þ ∂xJix 1⁄4
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