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Duality symmetry of the $p$-form effective action and super trace of the twisted de Rham complex
Peter B. Gilkey, Klaus Kirsten, Dmitri Vassilevich and Andrei Zelnikov
We consider quantum $p$-form fields interacting with a background dilaton. We calculate the variation with respect to the dilaton of a difference of the effective actions in the models related by a duality transformation. We show that this variation is defined essentially by the supertrace of the twisted de Rham complex. The supertrace is then evaluated on a manifold of an arbitrary dimension, with or without boundary.