TCFHs, hidden symmetries and type II theories

TL;DR

This paper introduces twisted covariant form hierarchies for type II supergravities, revealing hidden symmetries and integrability properties of supersymmetric backgrounds and brane solutions.

Contribution

It develops the TCFH framework for type IIA and IIB supergravities and analyzes hidden symmetries and integrability in various supergravity backgrounds.

Findings

All form bilinears satisfy the conformal Killing-Yano equation.

Geodesic flow on spherically symmetric backgrounds is completely integrable.

Form bilinears generate hidden symmetries for probe actions.

Abstract

We present the twisted covariant form hierarchies (TCFH) of type IIA and IIB 10-dimensional supergravities and show that all form bilinears of supersymmetric backgrounds satisfy the conformal Killing-Yano equation with respect to a TCFH connection. We also compute the Killing-St\"ackel, Killing-Yano and closed conformal Killing-Yano tensors of all spherically symmetric type II brane backgrounds and demonstrate that the geodesic flow on these solutions is completely integrable by giving all independent charges in involution. We then identify all form bilinears of common sector and D-brane backgrounds which generate hidden symmetries for particle and string probe actions. We also explore the question on whether charges constructed from form bilinears are sufficient to prove the integrability of probes on supersymmetric backgrounds.