Imperial College

At the leading order, the low-energy effective field equations in string

theory admit solutions of the form of products of Minkowski spacetime and a

Ricci-flat Calabi-Yau space. The equations of motion receive corrections at

higher orders in \alpha', which imply that the Ricci-flat Calabi-Yau space is

modified. In an appropriate choice of scheme, the Calabi-Yau space remains

Kahler, but is no longer Ricci-flat. We discuss the nature of these

corrections at order {\alpha'}^3, and consider the deformations of all the

known cohomogeneity one non-compact Kahler metrics in six and eight

dimensions. We do this by deriving the first-order equations associated with

the modified Killing-spinor conditions, and we thereby obtain the modified

supersymmetric solutions. We also give a detailed discussion of the boundary

terms for the Euler complex in six and eight dimensions, and apply the

results to all the cohomogeneity one examples. Additional material will be

presented concerning the case of holonomy G_2.