GRAVITY AND GLOBAL SYMMETRIES

There exists a widely held notion that gravitational effects can stron gly violate global symmetries. If this is correct, it may lead to many important consequences. We 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 fact or g less than or similar to 10(-82). One could hope that this problem disappears if one represents the global symmetry of a pseudoscalar ax ion held as a gauge symmetry of the Ogievetsky-Polubarinov-Kalb-Ramond antisymmetric tenser field. We show, however, that this gauge symmetr y does not protect the axion mass from quantum corrections. The amplit ude of gravitational effects violating global symmetries could be stro ngly suppressed by e(-S), where S is the action of a wormhole which ma y absorb the global charge. Unfortunately, in a wide variety of theori es based on the Einstein theory of gravity the action appears to be fa irly small, S similar to 10. However, we find that the existence of wo rmholes and the value of their action are extremely sensitive to the s tructure of space on the nearly Planckian scale. We consider several e xamples (Kaluza-Klein theory, conformal anomaly, R(2) terms) which sho w that modifications of the Einstein theory on the length scale l less than or similar to 10M(p)(-1) may strongly suppress violation of glob al symmetries. We find also that in string theory there exists an addi tional suppression oi topology change by the factor e(-)8 pi 2/g2 This effect is strong enough to save the axion theory for the natural valu es of the stringy gauge coupling constant.