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Hodge correlators. II. (English) Zbl 1217.14007

Author’s abstract: “We define Hodge correlators for a compact Kähler manifold \(X\). They are complex numbers which can be obtained by perturbative series expansion of a certain Feynman integral which we assign to \(X\). We show that they define a functorial real mixed Hodge structure on the rational homotopy type of \(X\).
The Hodge correlators provide a canonical linear map from the cyclic homomogy of the cohomology algebra of \(X\) to the complex numbers.
If \(X\) is a regular projective algebraic variety over a field \(k\), we define, assuming the motivic formalism, motivic correlators of \(X\). Given an embedding of \(k\) into complex numbers, their periods are the Hodge correlators of the obtained complex manifold.
Motivic correlators lie in the motivic coalgebra of the field \(k\). They come togerther with an explicit formula for their coproduct in the motivic Lie coalgebra.”

MSC:

14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14D07 Variation of Hodge structures (algebro-geometric aspects)
81T99 Quantum field theory; related classical field theories
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