Euclidean Wormholes in String Theory

TL;DR

The paper demonstrates that, in toroidally compactified type II string theory, axionic Euclidean wormholes can exist non-singularly in D≤6 and, in D=6, can be embedded into AdS3×S3×T^4 with a well-defined CFT dual. It shows that wormhole existence requires sufficiently long timelike geodesics in the moduli space and analyzes the action of these solutions, finding it smaller than the corresponding instanton pair. A detailed treatment of path-integral subtleties reveals that, when projected onto fixed charges, the semiclassical expansion requires flipping axion kinetic terms, and the resulting wormhole action is computed to compare with instanton configurations. The authors argue that AdS/CFT appears incompatible with Coleman’s α-parameter interpretation, signaling a paradox and suggesting that such wormhole saddles do not contribute in the string-theory realization of quantum gravity, or require a different conceptual understanding.

Abstract

We show that toroidal compactification of type II string theory to six dimensions admits axionic euclidean wormhole solutions. These wormholes can be inserted into $AdS_3 \times S^3 \times T^4$ backgrounds, which have a well-defined CFT dual. AdS/CFT duality then suggests that the wormhole solutions cannot be interpreted using $α$ parameters as originally suggested by Coleman.