Wormholes and the imaginary distance bound

Abstract

Some of the simplest wormhole solutions involve massless scalar fields that take imaginary values. Massless fields can be interpreted as coupling constants in asymptotically flat or asymptotically AdS gravity theories. We argue that wormhole effects imply an imaginary distance bound, an upper limit for the analytic continuation of the theory to imaginary values of these couplings. In string theory examples, we find explicit effects that render the low-energy theory invalid either before or precisely at this wormhole limit. We argue that the existence of such effects enforcing the distance bound is a general feature of string theories containing wormholes. In some cases, the bounds we discuss coincide with the weak gravity conjecture, and with the Kontsevich-Segal-Witten condition on complex metrics.