Instantons and Wormholes In Minkowski and (A)dS Spaces

TL;DR

This work analyzes instanton and wormhole solutions in $d$-dimensional gravity coupled to an axion–dilaton system across $\Lambda=0,\pm$. By exploiting an $O(d)$-invariant ansatz and a key first-integral constraint, it derives the conditions under which non-singular solutions exist and identifies a critical dilaton coupling $|b|<b_c$ governing regular wormholes. Instantons are shown to exist in flat and AdS spaces but are precluded in dS due to dilaton singularities, while wormholes require careful balancing of $c$, $b$, and $\Lambda$ and exhibit topology changes via necks of finite size; AdS wormholes persist with regulated actions via boundary terms. The results have implications for non-perturbative effects in string theory and quantum gravity, including potential links to baby universes and holographic renormalization in AdS.

Abstract

Instanton and wormhole solutions are constructed in a d-dimensional gravity theory with an axion-dilaton pair of scalar fields. We discuss the cases of vanishing, positive and negative cosmological constant.