Abstract
We gauge the abelian hierarchy of tensor fields in 4D by a Lie algebra \( \mathfrak{g} \). The resulting non-abelian tensor hierarchy can be interpreted via a \( \mathfrak{g} \)-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.
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ArXiv ePrint: 1603.07362
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Becker, K., Becker, M., Linch, W.D. et al. Chern-Simons actions and their gaugings in 4D, N =1 superspace. J. High Energ. Phys. 2016, 97 (2016). https://doi.org/10.1007/JHEP06(2016)097
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DOI: https://doi.org/10.1007/JHEP06(2016)097