Higher derivative terms including the Ramond-Ramond five-form

Abstract

Superfield methods can be used to determine the precise way the self-dual five-form couples to the metric in the first non-trivial ${\alpha }^{\prime }$ corrections to type IIB supergravity. We explicitly compute the exact tensor structure of these terms. This requires extensive use of computing algorithms to reduce the complicated expressions that appear to a surprisingly simple form. Along the way we show a new method of computing Schouten identities. With this result we clarify under which conditions one may neglect the five-form higher derivative terms. We comment on corrections to the thermodynamics of charged black holes.

v2 - Numerical typos fixed, small text changes.

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