GRAVITY AND GLOBAL SYMMETRIES

TL;DR

This paper investigates how gravitational effects can violate global symmetries, especially in axion theories, and explores mechanisms like modifications of gravity and string theory to suppress these violations.

Contribution

It demonstrates that gravitational violations of global symmetries are highly sensitive to Planck-scale physics and proposes scenarios where such violations can be effectively suppressed.

Findings

Nonperturbative gravitational effects can strongly violate CP in axion theories.

Modifications to Einstein gravity at small scales can suppress global symmetry violations.

String theory introduces an exponential suppression factor that protects axion solutions.

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^{-{8\pi^2\over g^2}}. This effect is strong enough to save the axion theory for the natural values of the stringy gauge coupling constant.