Instantons and no wormholes in $AdS_3\times S^3 \times CY_2$

TL;DR

This paper classifies supergravity instantons in $AdS_3\times S^3 \times CY_2$, finding that regular Euclidean wormholes do not exist, while certain supersymmetric lightlike geodesics correspond to string instantons in the dual CFT.

Contribution

It provides a detailed classification of axion-related instantons in $AdS_3\times S^3 \times CY_2$, demonstrating the non-existence of regular wormholes and identifying supersymmetric instantons.

Findings

Wormholes are shown to be non-regular.

Lightlike geodesics include supersymmetric instantons.

Dual instantons correspond to worldsheet instantons in the D1-D5 CFT.

Abstract

We study supergravity instantons sourced by axion (and saxion) fields in the Euclidean $AdS_3\times S^3 \times CY_2$ 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 (generalisations of) D-instantons and spacelike geodesics are sub-extremal 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, lift to Euclidean strings wrapping 2-cycles in the CY$_2$. The dual of these instantons are expected to be worldsheet instantons of the D1-D5 CFT.