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

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 $n\le 8$, 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.

40 pages; v2: references added, typos corrected, to appear in PTEP

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Cited by in corpus (1)

• Born sigma model for branes in exceptional geometry