Exact operator bosonization of finite number of fermions in one space dimension

TL;DR

This paper presents an exact operator bosonization method for a finite number of fermions in one dimension, applicable to various Hamiltonians, with implications for string theory and matrix models.

Contribution

It introduces a novel exact bosonization technique for finite fermion systems in one dimension, accommodating interactions and arbitrary Hamiltonians.

Findings

Fermion number appears as an ultraviolet cutoff in the bosonized theory

The method applies to interacting and noninteracting fermions with arbitrary Hamiltonians

Implications for string theory duals and matrix models are discussed

Abstract

We derive an exact operator bosonization of a finite number of fermions in one space dimension. The fermions can be interacting or noninteracting and can have an arbitrary hamiltonian, as long as there is a countable basis of states in the Hilbert space. In the bosonized theory the finiteness of the number of fermions appears as an ultraviolet cut-off. We discuss implications of this for the bosonized theory. We also discuss applications of our bosonization to one-dimensional fermion systems dual to (sectors of) string theory such as LLM geometries and c=1 matrix model.