Aspects of time evolution in $p$-form field theories

TL;DR

This paper investigates the stability of higher form fields, specifically 2- and 3-forms, revealing that self interactions can cause loss of hyperbolicity, affecting wave-like behavior and dynamic evolution.

Contribution

It demonstrates that self interactions in higher form fields lead to hyperbolicity loss, and shows that multiple self interaction terms can mitigate these issues.

Findings

Loss of hyperbolicity in self-interacting 2- and 3-form fields.

Regions of non-hyperbolic behavior can be reached dynamically from initial data.

Multiple self interaction terms can improve hyperbolicity stability.

Abstract

We show that higher form fields, specifically 2- and 3-forms in four spacetime dimensions, suffer from loss of hyperbolicity when they have self interaction. The equations of motion lose their wave-like characteristic in certain parts of the configuration space, and such problematic regions can also be reached dynamically from healthy initial data. These findings are analogous to recent results for vector fields, which are equivalently 1-forms, however, the details of the pathology can be different for higher forms. We also show that the possibility of more than one self interaction term in higher forms also leads to the amelioration of hyperbolicity problems.