Xenia de la Ossa

Mirror Symmetry for Two Parameter Models - II *

We describe in detail the space of the two Kahler parameters of the Calabi-Yau manifold P4(1,1,1,6,9)[18] by exploiting mirror symmetry. The large complex structure limit of the mirror, which corresponds to the classical large radius limit, is found by studying the monodromy of the periods about the discriminant locus, the boundary of the moduli space corresponding to singular Calabi-Yau manifolds. A symplectic basis of periods is found and the action of the Sp(6, Z) generators of the modular group is determined. From the mirror map we compute the instanton expansion of the Yukawa couplings and thes genralized N = 2 index, arriving at them numbers of instantons of genus zero and genus one of each bidegree. We find that these numbers can be negative, even in genus zero. We also investigate an SL(2, Z) symmetry that acts on a boundary of the moduli space.

Duality symmetries from non-abelian isometries in string theory

Abstract In string theory it is known that abelian isometries in the σ-model lead to target space duality. We generalize this duality to background with non-abelian isometries. The procedure we follow consist of gauging the isometries of the original action and constraining the field strength F to vanish. This new action generates dual theories by integrating over either the Lagrange multipliers that set F = 0 or the gauge fields. We find that this new duality transformation maps spaces with non-abelian isometries to spaces that may have no isometries at all. This suggests that duality symmetrics in string theories need to be understood in a more general context without regard to the existence of continuous isometries on the target space (this is also indicated by the existence of duality in string compactifications on Calabi-Yau manifolds which have no continuous isometries). Physically interesting examples to which our formalism apply are the Schwarzschild metric and the 4D charged dilatonic black hole. For these spherically symmetric black holes in four dimensions, the dual backgrounds are presented and explicitly shown to be new solutions of the leading order string equations. Some of these new backgrounds are found to have no continuous isometries (except for time translations) and also have naked singularities.

Periods for Calabi-Yau and Landau-Ginzburg vacua☆

Abstract The complete structure of the moduli space of Calabi-Yau manifolds and the associated Landau-Ginzburg theories, and hence also of the corresponding low-energy effective theory that results from (2, 2) superstring compactification, may be determined in terms of certain holomorphic functions called periods. These periods are shown to be readily calculable for a great many such models. We illustrate this by computing the periods explicitly for a number of classes of Calabi-Yau manifolds. We also point out that it is possible to read off from the periods certain important information relating to the mirror manifolds.

Holomorphic Bundles and the Moduli Space of N=1 Supersymmetric Heterotic Compactifications

A bstractWe describe the first order moduli space of heterotic string theory compactifications which preserve N =1 supersymmetry in four dimensions, that is, the infinitesimal parameter space of the Strominger system. We establish that if we promote a connection on T X to a field, the moduli space corresponds to deformations of a holomorphic structure D¯

G flux, supersymmetry and spin(7) manifolds

\overline{D}

The heterotic superpotential and moduli

on a bundle Q

Calabi-Yau manifolds over finite fields. 1.

\mathcal{Q}