We give a geometric description of supersymmetric gravity/(non-)abelian p-form hierarchies in superspaces with 4D, N = 1 super-Poincaré invariance. These hierarchies give rise to Chern-Simons-like invariants, such as those of the 5D, N = 1 graviphoton and the eleven-dimensional 3-form but also generalizations such as Green-Schwarz-like/BF -type couplings. Previous constructions based on prepotential superfields are reinterpreted in terms of p-forms in superspace thereby elucidating the underlying geometry. This vastly simplifies the calculations of superspace field-strengths, Bianchi identities, and Chern-Simons invariants. Using this, we prove the validity of a recursive formula for the conditions defining these actions for any such tensor hierarchy. Solving it at quadratic and cubic orders, we recover the known results for the BF -type and cubic Chern-Simons actions. As an application, we compute the quartic invariant ∼ AdAdAdA +.. relevant, for example, to seven-dimensional supergravity compactifications.
CITATION STYLE
Becker, K., Becker, M., Linch, W. D., Randall, S., & Robbins, D. (2017). All Chern-Simons invariants of 4D, N = 1 gauged superform hierarchies. Journal of High Energy Physics, 2017(4). https://doi.org/10.1007/JHEP04(2017)103
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