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International conference «Integrable systems and applications» in honour of M. A. Olshanetsky 80-th birthday
December 11, 2018 11:10–11:40, Moscow, Steklov Mathematical Institute, Gubkina 8, Conference hall
 


Special geometry on the Moduli space of Calabi-Yau manifolds, Localization and Two-Sphere partition function of GLSM

A. Belavin
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MP4 363.7 Mb

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A. Belavin
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Abstract: The requirement the Space-time supersymmetry in the String theory is equivalent to the geometrical condition of the compactification 6 of 10 dimentions on Calabi-Yau(CY) threefold. The properties of the Effective Lagrangian of the model, which describes the massless sector, are defined in terms of the so-called Special Kahler geometry on CY moduli space. I describe a new approach for computing the Special Kahler geometry based on the relation of Landau-Ginzburg superpotential of the model with a Frobenius manifold structure on the CY moduli space. I'l show how apply this approach for computing the Kahler metric on moduli space of the Calabi-Yau threefolds of Fermat type. Also I show how the Kahler potentials are connected with the partition functions of the $N=(2,2)$ Gauged Linear Sigma-Models on Two-Sphere.

Language: English

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