GRAVITY AND GLOBAL SYMMETRIES

TL;DR

The paper analyzes how gravity interacts with global symmetries, focusing on the axion and Peccei–Quinn mechanism. It shows that gravity-induced global-symmetry violation is controlled by the Euclidean wormhole action $S$, with CP restoration requiring $S\gtrsim190$ (suppression $e^{-S}$); dualizing to a 2-form gauge description does not, by itself, protect the axion mass. By exploring various gravitational modifications—Kaluza–Klein scenarios, conformal anomaly, $R^2$ terms, and string-inspired topological contributions—the authors identify mechanisms that can substantially increase $S$ and suppress topology-changing processes, potentially preserving global symmetries. They derive and analyze wormhole solutions with fixed and dynamical scalar fields, showing that in many models the action remains too small to solve the problem, but in others (notably with large extra dimensions or strong topological suppression) the danger can be mitigated. The work highlights a path to reconciling light axions with quantum gravity and outlines experimentally relevant implications for axion phenomenology and Planck-scale physics.

Abstract

There exists a widely spread notion that gravitational effects can strongly violate global symmetries. It may lead to many important consequences. We will argue, in particular, that nonperturbative gravitational effects in the axion theory lead to a strong violation of CP invariance unless they are suppressed by an extremely small factor 10^{-82}. One could hope that this problem disappears if one represents the global symmetry of a pseudoscalar axion field as a gauge symmetry of the Ogievetsky-Polubarinov-Kalb-Ramond antisymmetric tensor field. We will show, however, that this gauge symmetry does not protect the axion mass from quantum corrections. The amplitude of gravitational effects violating global symmetries could be strongly suppressed by e^{-S}, where S is the action of a wormhole which may eat the global charge. Unfortunately, in a wide variety of theories based on the Einstein theory of gravity the action appears to be fairly small, S = O(10). However, we have found that the existence of wormholes and the value of their action are extremely sensitive to the structure of space on the nearly Planckian scale. We consider several examples (Kaluza-Klein theory, conformal anomaly, R^2 terms) which show that modifications of the Einstein theory on the length scale l ~ 10 M_P^{-1} may strongly suppress violation of global symmetries. We have found also that in string theory there exists an additional suppression of topology change by the factor e^{-{8π^2\over g^2}}. This effect is strong enough to save the axion theory for the natural values of the stringy gauge coupling constant.