Superforms in six-dimensional superspace

Abstract

We investigate the complex of differential forms in curved, six-dimensional, N = (1,0) superspace. The superconformal group acts on this complex by super-Weyl transformations. An ambi-twistor-like representation of a second conformal group arises on a pure spinor subspace of the cotangent space. The p-forms are defined by super-Weyl-covariant tensor fields on this pure spinor subspace. The on-shell dynamics of such fields is superconformal. We construct the superspace de Rham complex by successively obstructing the closure of forms. We then extend the analysis to composite forms obtained by wedging together forms of lower degree. Finally, we comment on applications to integration in curved superspace and propose a superspace formulation of the abelian limit of the nonabelian tensor hierarchy of N = (1,0) superconformal models.

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© 2015 The Authors. Published for SISSA by Springer. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Received: March 7, 2016; Accepted: April 19, 2016; Published: May 3, 2016. It is a pleasure to thank Igor Bandos and Daniel Butter for discussions of their work, Brenno Carlini Vallilo for discussions and collaboration relating this work to the ambitwistor string of reference [57], and Jim Gates for encouragement, support, and references. We are especially indebted to Gabriele Tartaglino-Mazzucchelli for vetting this manuscript, his emphasis of subtle points we had not appreciated regarding integration in curved superspace, and his help with references and Robert Wimmer for carefully reading a previous version of this work, detailed discussions clarifying aspects of the non-abelian tensor hierarchy, and many suggestions for improving the presentation. WDL3 also thanks Stephen Randall for discussions and collaboration on closely-related work that illuminated many confusing aspects regarding superspace cohomology not addressed in the first version of this manuscript, and Richard Wentworth for continuing discussions that have lead to a deeper mathematical understanding of the tools developed and exploited herein. This work was partially supported by the National Science Foundation grants PHY-0652983 and PHY-0354401 and FONDECYT (Chile) grant number 11100425. CA is supported by the UNAB-DCF M. Sc. scholarship. WDL3 is partially supported by the UMCP Center for String & Particle Theory. AKR acknowledges participation in the 2013 Student Summer Theoretical Physics Research Session. WDL3 is grateful to the Simons Center for Geometry and Physics for hospitality during the xii Simons Workshop.

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Submitted - 1402.4823v1.pdf

Published - art_10.1007_JHEP05_2016_016.pdf

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