Holographic RG flows and wormholes from sinusoidal scalars

Abstract

We study semiclassical geometries induced by turning on identical sinusoidal scalar sources on two asymptotic anti-de Sitter (AdS) boundaries. Varying the source strength, we find that large and small wormhole solutions appear beyond a certain threshold. Above this threshold, the large wormhole is always the dominant saddle in the two-boundary gravitational path integral; there is no regime where wormholes are subdominant. Under the ensemble interpretation of the gravitational path integral, this implies that once wormhole solutions exist, the putative ensemble has exponentially large fluctuations relative to the mean. This is unlike previously studied examples of wormholes sourced by inhomogeneous matter which have a region in parameter space where wormholes are subdominant, and therefore the ensemble is sharply concentrated around the mean. Interpreting the bulk geometries as holographic renormalization group (RG) flows, we also find that the sinusoidal modulation of scalar boundary sources results in effective holographic $\beta$-functions which are multivalued, indicating exotic RG flows. In particular, disconnected geometries correspond to flows that return to the starting fixed point in the infrared, while wormholes describe flows to a gapped phase in the infrared.