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
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Submission date: 16. Sep. 2002
Pages: 20
published in: Nuclear Physics (Amsterdam) / B, 648 (2003) 3, p. 542-556 
PACS-Numbers: 02.40.-k, 04.62.+v, 11.15.-q
Keywords and phrases: dualities, dilaton, heat trace asymptotics
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Abstract:
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.