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All Chern-Simons invariants of 4D, N = 1 gauged superform hierarchies

  • Katrin Becker
  • Melanie Becker
  • William D. LinchIII
  • Stephen RandallEmail author
  • Daniel Robbins
Open Access
Regular Article - Theoretical Physics

Abstract

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.

Keywords

Superspaces Chern-Simons Theories Differential and Algebraic Geometry Supergravity Models 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Katrin Becker
    • 1
  • Melanie Becker
    • 1
  • William D. LinchIII
    • 1
  • Stephen Randall
    • 2
    Email author
  • Daniel Robbins
    • 3
  1. 1.George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and AstronomyTexas A&M UniversityCollege StationU.S.A.
  2. 2.Department of PhysicsUniversity of CaliforniaBerkeleyU.S.A.
  3. 3.Department of PhysicsUniversity at AlbanyAlbanyU.S.A.

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