Fourier–Laplace transform of a variation of polarized complex Hodge structure, II

Abstract

We show that the limit, by rescaling, of the 'new supersymmetric index' attached to the Fourier–Laplace transform of a polarized variation of Hodge structure on a punctured affine line is equal to the spectral polynomial attached to the same object. We also extend the definition by Deligne of a Hodge filtration on the de Rham cohomology of a exponentially twisted polarized variation of complex Hodge structure and prove a $E_1$-degeneration property for it.