A Monodromy from London

TL;DR

The paper argues that large-field axion monodromy inflation can be consistently realized within a massive $U(1)$ 4-form gauge theory, protected by a hidden gauge symmetry that prevents dangerous UV and gravitational corrections. It develops a detailed field-theoretic treatment, first via a warmup with a massive vector and then with massive 3-forms, showing good high-energy behavior, radiative stability, and a dual axion description through Julia-Toulouse-type condensates. The analysis covers effective field theory corrections (both $F^{2k}$ and $A^{2k}$ terms), potential inflationary flattening mechanisms, and the crucial role of discrete gauge invariance in enforcing monodromy and protecting large field excursions. The discussion also engages the Weak Gravity Conjecture and membranes, outlining how UV completions—potentially string-theoretic—could realize the required mass scales and dynamics. Overall, the work provides a coherent EFT framework that supports robust large-field inflation models anchored by gauge symmetries and defect condensation, with tangible implications for UV sensitivity and observational signatures.

Abstract

We focus on the massive gauge theory formulation of axion monodromy inflation. We argue that a gauge symmetry hidden in these models is the key protection mechanism from dangerous corrections from both field theory and gravitational dynamics. The effective theory of large field inflation is a dual to a massive U(1) 4-form gauge theory, which is similar to a massive gauge theory description of superconductivity. The gauge theory explicitly realizes the old Julia-Toulouse proposal for a low energy description of a gauge theory in a defect condensate. While we work mostly with the example of quadratic axion potential induced by flux monodromy, we discuss how other types of potentials can arise from inclusion of gauge invariant corrections to the theory.