Wormholes and the imaginary distance bound

TL;DR

The paper explores how wormhole solutions involving imaginary scalar fields impose an upper limit on the analytic continuation of coupling constants, with implications for string theory and related conjectures.

Contribution

It introduces the concept of an imaginary distance bound caused by wormhole effects and demonstrates its relevance in string theory examples and existing theoretical bounds.

Findings

Wormhole effects imply an upper limit for imaginary coupling values.

Explicit string theory examples show the low-energy theory becomes invalid at the bound.

The bounds relate to the weak gravity conjecture and the Kontsevich-Segal-Witten condition.

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.