Topological Excitations in the Thirring model

TL;DR

This paper investigates the quantization of the massless Thirring model on the light-cone, revealing topological excitations that lead to chiral symmetry breaking and depend on boundary conditions and coupling.

Contribution

It demonstrates the emergence of topological excitations in the light-cone quantized Thirring model and their role in chiral symmetry breaking, a novel insight into the model's quantum structure.

Findings

Topological excitations resemble abelian instantons for left-handed fermions.

Chiral symmetry is broken due to these topological excitations.

The conserved topological charge is quantized, varying with boundary conditions and coupling.

Abstract

The quantization of the massless Thirring model in the light-cone using functional methods is considered. The need to compactify the coordinate $x^-$ in the light-cone spacetime implies that the quantum effective action for left-handed fermions contains excitations similar to abelian instantons produced by composite of left-handed fermions. Right-handed fermions don't have a similar effective action. Thus, quantum mechanically, chiral symmetry must be broken as a result of the topological excitations. The conserved charge associated to the topological states is quantized. Different cases with only fermionic excitations or bosonic excitations or both can occur depending on the boundary conditions and the value of the coupling.