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Local B-model and mixed Hodge structure. (English) Zbl 1229.81243
Summary: We study the mixed Hodge theoretic aspects of the B-model side of local mirror symmetry. Our main objectives are to define an analogue of the Yukawa coupling in terms of the variations of the mixed Hodge structures and to study its properties. We also describe a local version of Bershadsky-Cecotti-Ooguri-Vafa’s holomorphic anomaly equation.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14D07 Variation of Hodge structures (algebro-geometric aspects)
58A14 Hodge theory in global analysis
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