Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-04-23
Journ\'ees de G\'eom\'etrie Alg\'ebrique d'Orsay (Juillet 1992), Ast\'erisque, vol. 218, 1993, pp. 243-271
Physics
High Energy Physics
High Energy Physics - Theory
25 pp., LaTeX 2.09 with AmS-Fonts
Scientific paper
We study moduli spaces of nonlinear sigma-models on Calabi-Yau manifolds, using the one-loop semiclassical approximation. The data being parameterized includes a choice of complex structure on the manifold, as well as some ``extra structure'' described by means of classes in H^2. The expectation that this moduli space is well-behaved in these ``extra structure'' directions leads us to formulate a simple and compelling conjecture about the action of the automorphism group on the K\"ahler cone. If true, it allows one to apply Looijenga's ``semi-toric'' technique to construct a partial compactification of the moduli space. We explore the implications which this construction has concerning the properties of the moduli space of complex structures on a ``mirror partner'' of the original Calabi-Yau manifold. We also discuss how a similarity which might have been noticed between certain work of Mumford and of Mori from the 1970's produces (with hindsight) evidence for mirror symmetry which was available in 1979. [The author is willing to mail hardcopy preprints upon request.]
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