Higher derivative terms including the Ramond-Ramond five-form

TL;DR

The work computes the exact α'^3 corrections to type IIB supergravity that couple the metric to the self-dual Ramond-Ramond five-form, using a superfield reduction to determine the tensor structure and projecting onto the 770 ⊕ 1050^+ representations. It develops a comprehensive Cadabra-based workflow with Young-projection and Schouten-identity techniques to produce explicit C^4, C^3T, C^2T^2, CT^3, and T^4 corrections, including self-duality constraints. It shows that highly supersymmetric backgrounds often receive no corrections in this sector, and demonstrates the importance of the full R^4-type corrections for certain backgrounds, especially in black hole thermodynamics and AdS/CFT contexts. The results enable precise corrections to thermodynamic quantities and shed light on how RR five-form contributions modify the strong-coupling dynamics of N=4 SYM via holography.

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 $α'$ 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.