Fermionic determinant as an overlap between bosonic vacua

TL;DR

This paper presents a novel way to express fermionic determinants as overlaps between bosonic vacua, potentially offering new tools for lattice field theory and bosonization techniques.

Contribution

It introduces a new bosonic overlap representation of Dirac determinants in even dimensions, differing from existing fermionic approaches.

Findings

Represents Dirac determinants as bosonic vacuum overlaps.

Provides a potential alternative for bosonization in lattice theories.

May facilitate new computational methods in quantum field theory.

Abstract

We find a representation for the determinant of a Dirac operator in an even number $D= 2 n$ of Euclidean dimensions as an overlap between two different vacua, each one corresponding to a bosonic theory with a quadratic action in $2 n + 1$ dimensions, with identical kinetic terms, but differing in their mass terms. This resembles the overlap representation of a fermionic determinant (although bosonic fields are used here). This representation may find applications to lattice field theory, as an alternative to other bosonized representations for Dirac determinants already proposed.