On supersymmetric Chern-Simons-type theories in five dimensions

Abstract

We present a closed-form expression for the supersymmetric non-Abelian Chern-Simons action in conventional five-dimensional N = 1 superspace. Our construction makes use of the superform formalism to generate supersymmetric invariants. Similar ideas are applied to construct supersymmetric actions for off-shell supermultiplets with an intrinsic central charge. In particular, the large tensor supermultiplet is described in superspace for the first time.

Superforms in five-dimensional, N = 1 superspace

“…Centrallyextended 5D superspace was investigated in [46] where the central charge was gauged and several superforms were constructed; their relationship to the forms presented here is also JHEP05(2015)049 of interest. Curved superspaces are another avenue for future study as we consider how such spaces fit into the general discussion of superform constraints and dimensional reduction.…”

Superforms in six-dimensional superspace

“…In curved superspaces or in flat superspace of dimensions other than four, partial results may be found throughout the literature, with interesting developments in four and five dimensions being reported as recently as last year [4][5][6][7][8]. Systematic studies of the closely related integral invariants in various dimensions are being carried out by Howe and his collaborators (e.g.…”

“…4 The differentials ∂ s and ∂ ψ do not commute with supersymmetry transformations. To get supersymmetrically covariant p-form components, we must replace coordinate derivatives by supercovariant derivatives.…”

Effective actions in N = 1 $$ \mathcal{N}=1 $$ , D5 supersymmetric gauge theories: harmonic superspace approach

“…Here there exists only a unique definition of the variation of the SCS action with respect to an infinitesimal deformation of the gauge potential V ++ . However, as it was noted in [62], it is unknown how to integrate this variation in a closed form to obtain the action as an integral over the superspace. The component formulation of the non-Abelian SCS model can be constructed in the framework of the superform approach [62], where a closed-form expression for the non-Abelian SCS…”

“…All these harmonic superspace formulations in space-time dimensions 4, 5 and 6 look almost analogous modulo some details. In a series of papers [58][59][60][61][62] an extensive program of constructing the manifestly supersymmetric formulation for the 5D, N = 1 supergravity-matter models was realized and the universal procedures to construct manifestly 5D supersymmetric action functionals for a different supermultiples were developed. These superfield results are in agreement with the earlier component considerations of the same models [63][64][65].…”