Twisted covariant form hierarchies and hidden symmetries

Abstract

Recently, it was shown that the conditions imposed on the Killing spinors bilinears by the gravitino Killing spinor equation in any supergravity theory can be arranged in a geometric structure callled Twisted Covariant Form Hierarchy (TCFH), which in turn implies that they satisfy a Generalised Conformal Killing-Yano equation. It has been known for a while that Killing-Yano tensors generate symmetries in spinning particle actions and they are related to hidden symmetries. This raises the question on whether supersymmetry is closely related to integrability. In this talk we explore the hidden symmetries and TCFH’s of 4D, 5D and 11D supergravities, giving some partial answers to this question.