Thin-shell wormholes in AdS$_5$ and string dioptrics

Abstract: We consider string probes in a traversable wormhole geometry that connects two locally AdS$_5$ asymptotic regions. Holographically, this describes two interacting copies of a 4-dimensional gauge theory. We consider string configurations whose endpoints are located either in the same boundary or in the two different boundaries of the wormhole. A string with both endpoints in the same boundary is dual to a quark-antiquark pair charged under the same gauge field, while a string extending through the wormhole describes a pair of colored particles charged under two different gauge fields. When one considers a quark-antiquark pair in each boundary, the system undergoes a phase transition: While for small separation each pair of charges exhibits Coulomb interaction, for large separation the charges in different field theories pair up. This behavior had previously been observed in other geometric realizations such as locally AdS$_5$ wormhole solutions with hyperbolic throats. The geometries we consider here, in contrast, are stable thin-shell wormholes with flat codimension-one hypersurfaces at fixed radial coordinate. They appear as electrovacuum solutions of higher-curvature gravity theories coupled to Abelian gauge fields. The presence of the thin-shells produces a refraction of the string configurations in the bulk, leading to the presence of cusps in the phase space diagram. We discuss these and other features of the phase diagram, including the analogies and difference with other wormhole solutions considered in related contexts.