Chern-Simons actions and their gaugings in 4D, N =1 superspace

We consider Chern-Simons actions of Abelian tensor hierarchy of p-form gauge fields in four-dimensional N = 1 supergravity. Using conformal superspace formalism, we solve the constraints on the field strengths of the p-form gauge superfields in the presence of the tensor hierarchy. The solutions are expressed by the prepotentials of the p-form gauge superfields. We show the internal and superconformal transformation laws of the prepotentials. The descent formalism for the Chern-Simons actions is exhibited.

Section: Review Of the Covariant Approachmentioning

confidence: 99%

Abelian tensor hierarchy and Chern-Simons actions in 4D N $$ \mathcal{N} $$ = 1 conformal supergravity

Yokokura

2016

“…At this point the non-abelian tensor hierarchy is a g-equivariant super-de Rham complex of forms on X × Y . Its Chern-Simons-like invariant was studied in some detail and generality in [7]. We review the gauge transformations, g-covariant superfield strengths, Bianchi identities, and Chern-Simons action in section 3.1.…”

Section: Jhep12(2016)085mentioning

confidence: 99%

“…The first is the superspace Chern-Simons invariant (3.5) of the gauged tensor hierarchy of the eleven-dimensional 3-form. This tensor hierarchy is a g-equivariant superspace chain complex with g the algebra of diffeomorphisms on Y [6,7]. The second is a superspace version of the Hitchin functional for G 2 -structure manifolds (3.8).…”

Section: Jhep12(2016)085mentioning

confidence: 99%

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M-theory potential from the G 2 Hitchin functional in superspace

Becker

Guha

et al. 2016

Self Cite

Abstract:We embed the component fields of eleven-dimensional supergravity into a superspace of the form X × Y where X is the standard 4D, N = 1 superspace and Y is a smooth 7-manifold. The eleven-dimensional 3-form gives rise to a tensor hierarchy of superfields gauged by the diffeomorphisms of Y . It contains a natural candidate for a G 2 structure on Y , and being a complex of superforms, defines a superspace Chern-Simons invariant. Adding to this a natural generalization of the Riemannian volume on X × Y and freezing the (superspin-3 2 and 1) supergravity fields on X, we obtain an approximation to the eleven-dimensional supergravity action that suffices to compute the scalar potential. In this approximation the action is the sum of the superspace Chern-Simons term and a superspace generalization of the Hitchin functional for Y as a G 2 -structure manifold. Integrating out auxiliary fields, we obtain the conditions for unbroken supersymmetry and the scalar potential. The latter reproduces the Einstein-Hilbert term on Y in a form due to Bryant.

“…Nevertheless, it was explicitly shown that it does work for 10D super-Yang-Mills in [24]. More recently, the approach was extended to the far more subtle case of elevendimensional supergravity in [25][26][27][28][29][30].…”

mentioning

confidence: 99%

Five-dimensional supergravity in N = 1/2 superspace

Becker

Butter

et al. 2020

Self Cite

We construct 5D, N = 1 supergravity in a 4D, N = 1 superspace with an extra bosonic coordinate. This represents four of the supersymmetries and the associated Poincaré symmetries manifestly. The remaining four supersymmetries and the rest of the Poincaré symmetries are represented linearly but not manifestly. In the linearized approximation, the action reduces to the known superspace result. As an application of the formalism, we construct the A ∧ R ∧ R invariant in this superspace. arXiv:1909.09208v1 [hep-th]