Exactly solvable string compactifications on manifolds of SU( N) holonomy

Abstract

A variety of heterotic string compactifications on the K3 surface, manifolds of SU(3) holomony, and higher holomony manifolds, are solved exactly. An example of the quintic hypersurface in CP 4 is worked out in detail. It is conjectured, and demonstrated in part, that any supersymmetric compactification of the heterotic string with an N=2 superconformal theory is equivalent to a compactification on a manifold of SU( N) holonomy, and in particular an arbitrary gluing of the discrete models with c=9 gives a solvable heterotic string compactification on some Calabi-Yau manifold. Calabi-Yau compactifications are seen to be exact vacua of string theory, retaining their topological and geometrical characteristics. Previously unknown enhanced gauge symmetries are found to arise for certain backgrounds.