\theta-angle monodromy in two dimensions

TL;DR

This paper investigates heta-angle monodromy phenomena in various two-dimensional gauge theories, revealing how metastable vacua and meson masses depend on heta, with implications for understanding axion-like models.

Contribution

It provides a detailed analysis of heta-angle monodromy in 2D gauge theories, including explicit calculations of vacuum energy, mass gaps, and landscape structures across multiple models.

Findings

Metastable vacuum energy deviates from quadratic dependence on heta.

Meson masses decrease as a function of heta in certain models.

The landscape includes sectors with nonabelian heta terms in U(N) models.

Abstract

"\theta-angle monodromy" occurs when a theory possesses a landscape of metastable vacua which reshuffle as one shifts a periodic coupling \theta by a single period. "Axion monodromy" models arise when this parameter is promoted to a dynamical pseudoscalar field. This paper studies the phenomenon in two-dimensional gauge theories which possess a U(1) factor at low energies: the massive Schwinger and gauged massive Thirring models, the U(N) 't Hooft model, and the {\mathbb CP}^N model. In all of these models, the energy dependence of a given metastable false vacuum deviates significantly from quadratic dependence on \theta just as the branch becomes completely unstable (distinct from some four-dimensional axion monodromy models). In the Schwinger, Thirring, and 't Hooft models, the meson masses decrease as a function of \theta. In the U(N) models, the landscape is enriched by sectors with nonabelian \theta terms. In the {\mathbb CP}^N model, we compute the effective action and the size of the mass gap is computed along a metastable branch.