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Periods and duality symmetries in Calabi-Yau compactifications. (English) Zbl 1360.32009
Summary: We derive the period structure of several one-modulus Calabi-Yau manifolds. With this knowledge we then obtain the generators of the duality group and the mirror map that defines the physical variable \(t\) representing the radius of compactification. We also describe the fundamental region of \(t\) and discuss its relation with automorphic functions. As a byproduct of our analysis we compute the non-perturbative corrections of Yukawa couplings.

MSC:
32G20 Period matrices, variation of Hodge structure; degenerations
14J33 Mirror symmetry (algebro-geometric aspects)
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32G81 Applications of deformations of analytic structures to the sciences
32J81 Applications of compact analytic spaces to the sciences
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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