Instantons and no wormholes in AdS3×S3×CY2

Abstract

We study supergravity instantons sourced by axion (and saxion) fields in the Euclidean ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{S}^{3}\ifmmode\times\else\texttimes\fi{}{\mathrm{CY}}_{2}$ vacua of IIB supergravity. Such instantons are described by geodesic curves on the moduli space; the timelike geodesics can describe Euclidean wormholes, the lightlike geodesics describe (generalizations of) D instantons, and spacelike geodesics are subextremal versions thereof. We perform a concrete classification of such geodesics and find that, despite earlier claims, the wormholes fail to be regular. A subclass of the lightlike geodesics is supersymmetric and, up to dualities, lifts to Euclidean strings wrapping 2-cycles in the ${\mathrm{CY}}_{2}$. The dual of these instantons is expected to be worldsheet instantons of the D1--D5 conformal field theory.