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Factored Coset Approach to Bosonization in the Context of Topological Backgrounds and Massive Fermions

Manías, María Virginia, Carlos Naón, Trobo, Marta Liliana

Published Jun 14, 1997• 0 citations
OpenAlex

Abstract

We consider a recently proposed approach to bosonization in which the original fermionic partition function is expressed as a product of a G/G-coset model and a bosonic piece that contains the dynamics. In particular we show how the method works when topological backgrounds are taken into account. We also discuss the application of this technique to the case of massive fermions.

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We consider a recently proposed approach to bosonization in which the original fermionic partition function is expressed as a product of a G/G-coset model and a bosonic piece that contains the dynamics. In particular we show how the method works when topological backgrounds are taken into account. We also discuss the application of this technique to the case of massive fermions.
We discuss various bosonization schemes from a path integral perspective. Our analysis shows that the existence of different bosonization schemes, such as abelian bosonization of non-abelian models and non-abelian bosonization of fermions with colour and flavour indices, can be understood as different ways of factoring out a dynamically trivial coset which contains the fermions. From this perspective follows the importance of the coset model in ensuring the correct superselection rules on the bosonic level.
When a quantum field theory possesses topological excitations in a phase with spontaneously broken symmetry, these are created by operators which are non-local with respect to the order parameter. Due to non-locality, such disorder operators have non-trivial correlation functions even in free massive theories. In two dimensions, these correlators can be expressed exactly in terms of solutions of non-linear differential equations. The correlation functions of the one-parameter family of non-local operators in the free charged bosonic and fermionic models are the inverse of each other. We point out a simple derivation of this correspondence within the form factor approach
We use the recently developed tools for an exact bosonization of a finite number NNN of nonrelativistic fermions to discuss the classic Tomonaga problem. In the case of noninteracting fermions, the bosonized Hamiltonian naturally splits into an O(N)\mathrm{O}(N)O(N) piece and an O(1) piece. We show that in the large-NNN and low-energy limit, the O(N)\mathrm{O}(N)O(N) piece in the Hamiltonian describes a massless relativistic boson, while the O(1) piece gives rise to cubic self-interactions of the boson. At finite NNN and high energies, the low-energy effective description breaks down and the exact bosonized Hamiltonian must be used. We also comment on the connection between the Tomonaga problem and pure Yang-Mills theory on a cylinder. In the dual context of baby universes and multiple black holes in string theory, we point out that the O(N)\mathrm{O}(N)O(N) piece in our bosonized Hamiltonian provides a simple understanding of the origin of two different kinds of nonperturbative $\mathrm{O}({e}^{\ensuremath{-}N})$ corrections to the black hole partition function.
There are two different results concerning the functional relationship between the chemical potential of the 1D massive Thirring model and the misfit parameter of the 1D quantum sine-Gordon model which have been reported [4-7]. In order to investigate this problem, the Jordan boson representation of fermion field operators is used to obtain the bosonized expression of the 1D massive Thirring model. The equivalence of this model with the 1D quantum sine-Gordon model is proved, all zero-mode contributions taken into account. The problem of controversial results previously reported is solved. Thereafter, by means of Bethe-Ansatz method, a new expression for the critical curve of the commensurate-incommensurate transition in the two-dimensional sine-Gordon model is found.