String corrections leave gravitational instanton geometry intact but disturb its scalar fields

Self-dual gravitational instantons — smooth, curved Euclidean spacetimes that play a role in quantum gravity path integrals — are protected from metric deformation by the first α′ corrections coming from heterotic string theory, even though the accompanying scalar fields are not. Working within a four-dimensional action derived from compactified heterotic strings, the authors compute explicit scalar-field corrections for the Taub–NUT and Eguchi–Hanson spaces, construct the boundary terms needed for a well-posed variational problem, and show that the total Euclidean action of the Eguchi–Hanson instanton receives no net correction at first order in α′. They also identify a class of solutions analogous to D-instantons sitting on an unmodified gravitational instanton background.