Chern-Simons Actions and Their Gaugings in 4D, N=1 Superspace

Abstract

We gauge the abelian hierarchy of tensor fields in 4D by a Lie algebra. The resulting non-abelian tensor hierarchy can be interpreted via an equivariant chain complex. We lift this structure to N=1 superspace by constructing superfield analogs for the tensor fields, along with covariant superfield strengths. Next we construct Chern-Simons actions, for both the bosonic and N=1 cases, and note that the condition of gauge invariance can be presented cohomologically. Finally, we provide an explicit realization of these structures by dimensional reduction, for example by reducing the three-form of eleven-dimensional supergravity into a superspace with manifest 4D, N=1 supersymmetry.

40pp, v2 added references

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• The end of the p-form hierarchy
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Cited by in corpus (11)

• Eleven-Dimensional Supergravity in 4D, $N=1$ Superspace
• U(1) symmetric $\alpha$-attractors
• Abelian tensor hierarchy in 4D $\mathcal{N}=1$ conformal supergravity
• Five-dimensional Supergravity in N = 1/2 Superspace
• M-theory Potential from the $G_2$ Hitchin Functional in Superspace
• All Chern-Simons Invariants of 4D, N = 1 Gauged Superform Hierarchies
• N=1 Supercurrents of Eleven-dimensional Supergravity
• Abelian tensor hierarchy and Chern-Simons actions in 4D N=1 conformal supergravity
• Components of Eleven-dimensional Supergravity with Four Off-shell Supersymmetries
• 4D N=1 Kaluza-Klein superspace
• Linearized Off-shell 4+7 Supergeometry of 11D Supergravity