Instanton expansions and phase transitions

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