TCFHs, IIB warped AdS backgrounds and hidden symmetries

TL;DR

This paper develops twisted covariant form hierarchies on internal spaces of type IIB warped AdS backgrounds, revealing generalized conformal Killing-Yano equations and hidden symmetries relevant for particle probes and supersymmetric solutions.

Contribution

It introduces TCFHs on internal spaces of warped AdS backgrounds, generalizing conformal Killing-Yano equations and identifying hidden symmetries in specific geometries.

Findings

Form bilinears satisfy a generalized conformal Killing-Yano equation.

Hidden symmetries are generated for particle probes in certain backgrounds.

Examples include maximally supersymmetric AdS$_5$ and near horizon geometries.

Abstract

We present the twisted covariant form hierarchies (TCFHs) on the internal spaces of all type IIB warped AdS backgrounds. As a result we demonstrate that the form bilinears on the internal spaces satisfy a generalisation of the conformal Killing-Yano equation. We also explore some of the properties of the TCFHs, like for example the holonomy of the TCFH connections. In addition, we present examples where the form bilinears generate hidden symmetries for particle probes propagating on the internal spaces of some AdS backgrounds. These include the maximally supersymmetric AdS$_5$ solution as well as some of the near horizon geometries of intersecting IIB branes.