CP violation and modular symmetries - art. no. 056005

We reconsider the origin of CP violation in fundamental theory. Existing st ring models of spontaneous CP violation make ambiguous predictions, due to the arbitrariness of CP transformation and the apparent noninvariance of th e results under duality. We find a modular CP invariance condition, applica ble to any predictive model of spontaneous CP violation, which circumvents these problems; it strongly constrains CP violation by heterotic string mod uli. The dilaton is also evaluated as a source of CP violation, but is like ly experimentally excluded. We consider the prospects for explaining CP vio lation in strongly coupled strings and brane worlds.