Instanton Expansions and Phase Transitions

TL;DR

This paper investigates the breakdown of instanton expansions in axionic theories, revealing phase transition phenomena and proposing alternative descriptions that remain valid beyond traditional instanton control, with implications for the Weak Gravity Conjecture.

Contribution

It introduces a phase transition perspective to instanton expansions in axionic theories and offers new methods to describe the effective potential when instanton control is lost.

Findings

The theory undergoes a phase transition when instanton control fails.

Light states emerge in the breakdown region, affecting the effective potential.

Alternative expressions for the potential remain valid beyond instanton expansion control.

Abstract

A central object in any axionic theory is its periodic potential, which is typically generated by instantons. The goal of this paper is to understand what physically happens to the theory when we lose control of the potential's instanton expansion. We argue, using the Yang-Lee theory of phase transitions, that the theory breaks down in the classic sense: states become light. However, these states are not necessarily light for all values of the axion and there can be large regions where the effective description remains valid. We find alternative expressions for the effective potential in terms of the properties of these light states, which remain useful even when the instanton expansion breaks down, and thus initiate a push beyond the lamppost of large instanton actions. Most of these questions are motivated by the axionic Weak Gravity Conjecture, which we reformulate without reference to instanton actions. We also comment on its ability to constrain large-field axion inflation.