Non-topological fractional fermion number in the Jackiw-Rossi model

TL;DR

This paper demonstrates that the fermion number induced by vortices in the $(2+1)$-dimensional Jackiw-Rossi model is non-topological, challenging previous assumptions about its topological nature using a $1/m$ expansion and $ ext{eta}$-function analysis.

Contribution

It provides the first explicit calculation showing the non-topological nature of vortex-induced fermion number in the Jackiw-Rossi model.

Findings

Fermion number in the model is non-topological.

The usual topological proof of $ ext{eta}(0)$ does not apply.

Direct computation confirms the non-topological result.

Abstract

We compute the vacuum fermion current in $(2+1)$ dimensional Jackiw-Rossi model by using the $1/m$ expansion. The current is expressed through a weighted $\eta$-function with a matrix weight. In the presence of such a weight, the usual proof of topological nature of $\eta(0)$ is not longer applicable. Direct computations confirm the following surprising result: the fermion number induced by vortices in the Jackiw-Rossi model is \textit{not} topological.