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All Chern-Simons Invariants of 4D, N = 1 Gauged Superform Hierarchies | | Katrin Becker
; Melanie Becker
; William D. Linch III
; Stephen Randall
; Daniel Robbins
; | | Date: |
2 Feb 2017 | | Abstract: | We give a geometric description of supersymmetric gravity/(non-)abelian
$p$-form hierarchies in superspaces with 4D, $N = 1$ super-Poincar’e
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 $sim A dA dA dA + ldots$ relevant, for example,
to seven-dimensional supergravity compactifications. | | Source: | arXiv, 1702.0799 | | Services: | Forum | Review | PDF | Favorites | |
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