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

Euclidean anti-de Sitter (AdS) wormholes provide a natural setup for studying the anti-de Sitter/conformal field theory (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.