Exotic branes and mixed-symmetry potentials II: Duality rules and exceptional $p$-form gauge fields

TL;DR

This paper develops a systematic method to parameterize mixed-symmetry potentials in U-duality formulations of supergravity, deriving duality transformation rules and applying them to the dual graviton and generalized graviphoton.

Contribution

It introduces a new systematic approach to parameterize $p$-form fields involving mixed-symmetry potentials and derives their duality transformation rules.

Findings

Parameterization of mixed-symmetry potentials achieved.

Duality rules for these potentials systematically derived.

Application to dual graviton and generalized graviphoton demonstrated.

Abstract

In U-duality-manifest formulations, supergravity fields are packaged into covariant objects such as the generalized metric and $p$-form fields $\mathcal{A}_p^{I_p}$. While a parameterization of the generalized metric in terms of supergravity fields is known for U-duality groups $E_n$ with $n\leq 8$, a parameterization of $\mathcal{A}_p^{I_p}$ has not been fully determined. In this paper, we propose a systematic method to determine the parameterization of $\mathcal{A}_p^{I_p}$, which necessarily involves mixed-symmetry potentials. We also show how to systematically obtain the T- and S-duality transformation rules of the mixed-symmetry potentials entering the multiplet. As the simplest non-trivial application, we find the parameterization and the duality rules associated with the dual graviton. Additionally, we show that the 1-form field $\mathcal{A}_1^{I_1}$ can be regarded as the generalized graviphoton in the exceptional spacetime.