Quantum algebraic geometry of superstring compactifications

We investigate the algebrao-geometric structure which is inherent in 2-dimensional conformally invariant quantum field theories with N=2 supersymmetry, and its relation to the Calabi-Yau manifolds which appear in the so-called "large radius limit". Based on a careful comparison of the Kähler cone of Calabi-Yau manifolds and the moduli space of marginal chiral fields in string theory, we give a precise definition of this limit. The possibility of "flopping" between manifolds of different topology implies that the large radius limit of a given conformal model is ambiguous, and that the instantons in string theory could smooth out some of the singularities present in the classical moduli space. Since the mirror symmetry implies that the duality group of the stringy moduli space in a topological basis is at least Sp(b-3, Z)×Sp(b13, Z), we are able to identify the generalization of the "R → 1/R" symmetry in c=1 models to any (2,2) model. © 1991.

Duke Scholars

Author Paul Stephen Aspinwall Mathematics