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The Hodge Galois group is the Tannakian Galois group of the category of realmixed Hodge structures. It has a subgroup, called the twistor Galois group,which is the Galois group of the category of mixed twistor structures, definedby C. Simpson. It is isomorphic to a semidirect product of C* and the unipotentradical of the Hodge Galois group. We define a natural action of the twistorGalois group by A-infinity autoequivalences of the derived category ofcomplexes of sheaves with smooth cohomology on a compact smooth Kahler manifoldX. The action of C* is provided by Simpson's action on irreducible localsystems, and the action of the unipotent radical is given explicitly by theHodge correlators for irreducible local systems on X. The Hodge correlators canbe interpreted as correlators of cetrtain Feynman integrals. One should have asimilar construction for the whole derived category of all holonomic D-modules.

Hidden Hodge symmetries and Hodge correlators