Massive Schwinger model with a finite inductance: theta-(in)dependence, the U(1) problem, and low-energy theorems

TL;DR

This paper investigates the effects of an inductance term in a modified Schwinger model, showing that topological susceptibility vanishes and theta-dependence is suppressed, with implications for the U(1) problem and low-energy theorems.

Contribution

It introduces an inductance term into the Schwinger model and analyzes its impact on topological susceptibility and theta-dependence, revealing a global mode that alters topological properties.

Findings

Topological susceptibility vanishes in the model.

Theta-dependence is suppressed due to a global mode.

The U(1) problem remains unaffected by the inductance term.

Abstract

Gauge theories embedded into higher-dimensional spaces with certain topologies acquire inductance terms, which reflect the energy cost of topological charges accumulated in the extra dimensions. We compute topological susceptibility in the strongly-coupled two-flavor massive Schwinger model with such an inductance term and find that it vanishes, due to the contribution of a global low-energy mode (a ``global axion''). This is in accord with the general argument on the absence of theta-dependence in such topologies. Because the mode is a single oscillator, there is no corresponding particle, and the solution to the U(1) problem is unaffected.