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

Abstract

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.

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

“…The tensor hierarchy can be coupled to gravity by replacing D → D with the gravitationally covariant superspace derivative, covariantizing the measures as usual, and replacinḡ D 2 →D 2 −8R [16,17]. (Equivalently, one can replace D by the conformal superspace supergravity derivative [18,19].) Then, the complete component projection of the action can be computed straightforwardly, but for this paper we are interested only in the contribution to the scalar potential of the component theory.…”

“…As this is the correct potential for eleven-dimensional supergravity on X × Y , this observation relates topological M theory [22] to "physical" M-theory, and suggests the following construction of eleven-dimensional supergravity on X × Y to this order in the super-gravitino expansion (1.1): starting with the non-abelian tensor hierarchy, one defines on the space of 3-form field strength superfields the curved superspace generalization (3.8) of the Hitchin functional. To this one adds the ChernSimons super-invariant (3.5) in curved superspace [16] (see also [18,19]). Note that we cannot add a superpotential beyond the F-terms coming from the Chern-Simons action because the G 2 -structure metric is not chiral.…”

Dual formulations of vortex strings in a supersymmetric Abelian Higgs model

“…It will be convenient to use conformal SUGRA [65][66][67][68][69][70][71] when we discuss the dual transformations of ANO vortex strings, since the canonically normalized Einstein-Hilbert term can be obtained by the superconformal gauge-fixing without tedious super-Weyl rescalings [67]. In particular, the conformal superspace formalism [69] and p-form gauge theories in the conformal superspace [72,73] would be useful, since we can discuss dual transformations in a manifestly SUSY way.…”

Topological couplings in higher derivative extensions of supersymmetric three-form gauge theories

“…[28][29][30] as a review). The SUSY 3-form gauge theories were also extensively studied with various applications: gaugino condensation in SUSY Yang-Mills theories [31][32][33], coupling with a membrane [34][35][36], alternative formulation of old-minimal SUGRA [34,[37][38][39], Stückelberg coupling [40][41][42][43], topological coupling [42,44,45], complex 3-form gauge theories [35,36,39], extended SUSY [46], the cosmological constant problem [38], SUSY breaking [38,47,48], and inflationary models [44,49].…”

“…In the SUSY theories, the field strength of the 3-form gauge field can be embedded into an auxiliary field of a chiral superfield given by a real superfield [24]. The topological coupling is given by choosing appropriate superpotential [42,44,45]. This coupling was applied to SUGRA inflationary models [44,49].…”