Superforms in Simple 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 give a superspace formulation of the abelian limit of the non-abelian tensor hierarchy of $N=(1,0)$ superconformal models and propose a formulation of it as a Chern-Simons theory on the ambi-twistor-like superspace.

References in corpus (7)

• On conformal supergravity and projective superspace
• Five-dimensional N = 1 AdS superspace: Geometry, off-shell multiplets and dynamics
• New superconformal models in six dimensions: Gauge group and representation structure
• Explaining Pure Spinor Superspace
• Compactification of the Heterotic Pure Spinor Superstring I
• Pure Spinors and D=6 Super-Yang-Mills
• The Geometry of 6D, N = (1,0) Superspace and its Matter Couplings

Cited by in corpus (8)

• Invariants for minimal conformal supergravity in six dimensions
• The component structure of conformal supergravity invariants in six dimensions
• Curvature squared invariants in six-dimensional $\mathcal{N}=(1,0)$ supergravity
• Construction of 6D supersymmetric field models in N=(1,0) harmonic superspace
• A new approach to curved projective superspace
• The anomalous current multiplet in 6D minimal supersymmetry
• New superconformal multiplets and higher derivative invariants in six dimensions
• Superspace de Rham Complex and Relative Cohomology