UV and IR Effects in Axion Quality Control

Motivated by recent discussions and the absence of exact global symmetries in UV completions of gravity we re-examine the axion quality problem (and naturalness issues more generally) using antisymmetric Kalb-Ramond (KR) fields rather than their pseudoscalar duals, as suggested by string and higher dimensional theories. Two types of axions can be identified: a model independent $S$-type axion dual to a two form $B_{\mu\nu}$ in 4D and a $T$-type axion coming directly as 4D scalar Kaluza-Klein (KK) components of higher-dimensional tensor fields. For $T$-type axions our conclusions largely agree with earlier workers for the axion quality problem, but we also reconcile why $T$-type axions can couple to matter localized on 3-branes with Planck suppressed strength even when the axion decay constants are of order the KK scale. For $S$-type axions, we review the duality between form fields and massive scalars and show how duality impacts naturalness arguments about the UV sensitivity of the scalar potential. In particular UV contributions on the KR side suppress contributions on the scalar side by powers of $m/M$ with $m$ the axion mass and $M$ the UV scale. We re-examine how the axion quality problem is formulated on the dual side and compare to recent treatments. We study how axion quality is affected by the ubiquity of $p$-form gauge potentials (for both $p=2$ and $p=3$) in string vacua and identify two criteria that can potentially lead to a problem. We also show why most fields do not satisfy these criteria, but when they do the existence of multiple fields also provides mechanisms for resolving it. We conclude that the quality problem is easily evaded.