Fractons in Twisted Multiflavor Schwinger Model

TL;DR

This paper studies a modified 2D QED model with flavor-dependent boundary conditions, revealing fractional topological charges and their role in fermion condensate formation, with implications for non-abelian theories.

Contribution

It introduces a flavor-dependent boundary condition modification in 2D QED, showing fractional topological charges influence condensate formation and decay.

Findings

Fractional topological charge configurations contribute to the path integral.

Fermion condensate forms due to fractional topological charge.

Condensate diminishes as inverse power of the spatial length.

Abstract

We consider two-dimensional QED with several fermion flavors on a finite spatial circle. A modified version of the model with {\em flavor-dependent} boundary conditions $\psi_p(L) = e^{2\pi ip/ N} \psi_p(0)$, $p = 1, \ldots , N$ is discussed ($N $ is the number of flavors). In this case a non-contactable contour in the space of the gauge fields is {\em not} determined by large gauge transformations. The Euclidean path integral acquires the contribution from the gauge field configurations with fractional topological charge. The configuration with $\nu = 1/N$ is responsible for the formation of the fermion condensate $\langle\bar{\psi}_p \psi_p\rangle_0$. The condensate dies out as a power of $L^{-1}$ when the length $L$ of the spatial box is sent to infinity. Implications of this result for non-abelian gauge field theories are discussed in brief.