All Chern-Simons Invariants of 4D, N = 1 Gauged Superform Hierarchies

Abstract

We give a geometric description of supersymmetric gravity/(non-)abelian $p$-form hierarchies in superspaces with 4D, $N=1$ super-Poincare 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 $\sim AdAdAdA+\dots$ relevant, for example, to seven-dimensional supergravity compactifications.

arXiv comment31 pages; v2: added references

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Cited by in corpus (6)

• Five dimensional supergravity in N = 1 superspace
• Eleven-Dimensional Supergravity in 4D, $N=1$ Superspace
• U(1) symmetric $\alpha$-attractors
• Five-dimensional Supergravity in N = 1/2 Superspace
• N=1 Supercurrents of Eleven-dimensional Supergravity
• Components of Eleven-dimensional Supergravity with Four Off-shell Supersymmetries