Advances in Theoretical and Mathematical Physics

Volume 21 (2017)

Number 4

Mixed trTLEP-structures and mixed Frobenius structures

Pages: 977 – 1021

DOI: http://dx.doi.org/10.4310/ATMP.2017.v21.n4.a4

Author

Yota Shamoto (Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan)

Abstract

We introduce the notion of mixed trTLEP-structures and prove that a mixed trTLEP-structure with some conditions naturally induces a mixed Frobenius manifold. This is a generalization of the reconstruction theorem of Hertling and Manin. As a special case, we also show that a graded polarizable variation of mixed Hodge structure with $H^2$-generation condition gives rise to a family of mixed Frobenius manifolds. It implies that there exist mixed Frobenius manifolds associated to local B-models.

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