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Autores principales: Cappelli, Andrea, Maffi, Lorenzo, Villa, Riccardo
Formato: Preprint
Publicado: 2024
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Acceso en línea:https://arxiv.org/abs/2406.01787
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author Cappelli, Andrea
Maffi, Lorenzo
Villa, Riccardo
author_facet Cappelli, Andrea
Maffi, Lorenzo
Villa, Riccardo
contents Three-dimensional topological insulators can be described by an effective field theory involving two `hydrodynamic' Abelian gauge fields. The action contains a bulk topological BF term and a surface term, called loop model. This describes the massless 2+1 dimensional excitations and provides them with a semiclassical, yet non-trivial conformal invariant dynamics. Given that topological insulators are originally fermionic, this physical setting is ideal for realizing the bosonization of massless fermions in terms of gauge fields. Building on earlier analyses of the loop model, we find that fermions belong to the solitonic spectrum and can be described by Wilson lines, through the generalization of 1+1 dimensional vertex operators. Their correlation functions agree with conformal invariance. The bosonic loop model is then mapped into a fermionic theory by using the general construction of fermionic topological phases described in the literature. It requires the identification of the characteristic one-form $Z_2$ symmetry of the bosonic theory and its gauging, which originates the fermion number $(-1)^F$, the spin sectors and the time reversal symmetry obeying ${\cal T}^2=(-1)^F$. These results are detailed for the effective action and the partition function on the geometry $S^2\times S^1$.
format Preprint
id arxiv_https___arxiv_org_abs_2406_01787
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Bosonization of 2+1 dimensional fermions on the surface of topological insulators
Cappelli, Andrea
Maffi, Lorenzo
Villa, Riccardo
High Energy Physics - Theory
Strongly Correlated Electrons
Three-dimensional topological insulators can be described by an effective field theory involving two `hydrodynamic' Abelian gauge fields. The action contains a bulk topological BF term and a surface term, called loop model. This describes the massless 2+1 dimensional excitations and provides them with a semiclassical, yet non-trivial conformal invariant dynamics. Given that topological insulators are originally fermionic, this physical setting is ideal for realizing the bosonization of massless fermions in terms of gauge fields. Building on earlier analyses of the loop model, we find that fermions belong to the solitonic spectrum and can be described by Wilson lines, through the generalization of 1+1 dimensional vertex operators. Their correlation functions agree with conformal invariance. The bosonic loop model is then mapped into a fermionic theory by using the general construction of fermionic topological phases described in the literature. It requires the identification of the characteristic one-form $Z_2$ symmetry of the bosonic theory and its gauging, which originates the fermion number $(-1)^F$, the spin sectors and the time reversal symmetry obeying ${\cal T}^2=(-1)^F$. These results are detailed for the effective action and the partition function on the geometry $S^2\times S^1$.
title Bosonization of 2+1 dimensional fermions on the surface of topological insulators
topic High Energy Physics - Theory
Strongly Correlated Electrons
url https://arxiv.org/abs/2406.01787