Euclidean AdS wormholes and gravitational instantons in the Einstein-Skyrme theory

TL;DR

This paper demonstrates the existence of Euclidean AdS wormholes and gravitational instantons in Einstein-Skyrme theory, revealing new topological solutions with implications for holography and phase transitions.

Contribution

It introduces Euclidean AdS wormholes in Einstein-Skyrme theory and analyzes their properties, including free energy, stress tensor, and phase transitions, expanding the landscape of holographic topological solutions.

Findings

Wormholes in Einstein-Skyrme theory have constant free energy.

Holographic stress tensor vanishes, indicating BPS states.

Existence of phase transitions in gravitational instantons.

Abstract

Euclidean AdS wormholes provide a natural setup for studying the AdS/CFT correspondence with multiple boundaries. However, from a bottom-up perspective, they cannot be embedded in the four-dimensional Einstein-AdS-Maxwell theory if these boundaries have positive curvature. Nevertheless, Maldacena and Maoz showed that this obstruction could be circumvented by introducing merons in the four-dimensional Einstein-AdS-Yang-Mills theory. In this work, we show that Euclidean-AdS wormholes also exist in the four-dimensional Einstein-AdS-Skyrme theory, whose matter sector possesses a nontrivial baryonic charge. We compute its free energy and show that it does not depend on the integration constants whatsoever, resembling topological solitons. Additionally, we obtain its holographic stress tensor and show that it vanishes, allowing us to interpret this configuration as a holographic Bogomol'nyi-Prasad-Sommerfield (BPS) state. Other topologically nontrivial ground states in Einstein-Skyrme theory are found, such as gravitational instantons, representing the homotopically inequivalent vacua of the theory. We find that they develop Hawking-Page phase transitions above a critical temperature. Some of these solutions are periodic in Euclidean time, representing the gravitational analog of calorons in Yang-Mills theory.