Fermi-Bose Cancellation in Topologically Non-Trivial Backgrounds

TL;DR

This paper demonstrates that in topologically non-trivial backgrounds like solitons or instantons, fermion and boson spectra cancel at one-loop, generalizing previous specific results and linking zero modes to index theorems.

Contribution

It provides a model-independent proof of fermion-boson cancellation and clarifies the connection between zero modes and index theorems in such backgrounds.

Findings

Fermion and boson spectra cancel at one-loop in topological backgrounds.

The cancellation is model-independent and applies to a broad class of solitons and instantons.

The work establishes a general link between zero modes and index theorems.

Abstract

We show in a model-independent way that, in the background of a topological soliton or instanton that saturates a Bogomol'nyi bound, the fermion and boson excitation spectra of non-zero modes cancel at the one-loop level. This generalizes D'Adda and DiVecchia's result for some specific instanton models. Our method also establishes, again in a model-independent way, the generality of the connection between zero modes in topologically non-trivial backgrounds and index theorems.