Hierarchy of mechanics models

Abstract

Using the N =4 superspace approach in one dimension (time), we construct general N =8 supersymmetric mechanics actions for the multiplets (b, 8, 8−b) classified in hep-th/0406015, with the main focus on the previously unexplored cases of (8, 8, 0), (7, 8, 1) and (6, 8, 2) , as well as on (5, 8, 3) for completeness. N =8 supersymmetry of the action amounts to a harmonicity condition for the Lagrangian with respect to its superfield arguments. We derive the generic off-shell component action for the "root" multiplet (8,8, 0), prove that the actions for all other multiplets follow from it through automorphic dualities and argue that this hierarchical structure is universal. The bosonic target geometry in all cases is conformally flat, with a unique scalar potential (except for the root multiplet). We show that the N =4 superfield constraints respect the full R-symmetry and find the explicit realization of its quotient over the manifest R-symmetry on superfields and component fields. Several R-symmetric N =4 superfield Lagrangians with N =8 supersymmetry are either newly found or reproduced by a simple universal method.

Supersymmetric Chern–Simons vortex systems and extended supersymmetric quantum mechanics algebras

“…Moreover, extended supersymmetries serve as super-extensions of integrable models like Calogero-Moser systems, Landau-type models [23]. But one of the most salient feature of the N = 4 extended supersymmetric quantum algebra is that it can be connected to a generalized harmonic superspace [24][25][26][27][28][29][30][31][32][33], with the latter being a useful tool for N ≥ 4 supersymmetric model building. These harmonic space structures are linked to supersymmetric linear sigma models defined in the target space.…”

Effective symmetries of the minimal supermultiplet of theN= 8 extended worldline supersymmetry

“…[2,3,4,5]. The ultra-multiplet was introduced in a manifestly Spin(4)×Z 2 -symmetric notation; see below and in particular Appendix C. By means of a systematic component field redefinition by now known as node-raising/lowering [6,7,8], this supermultiplet is seen to be closely related to a family of supermultiplets, identifiable with the "root superfield" of Ref.…”

“…By "Z e 2 group" we then always mean just this Spin(1) = Z 2 . 4 The term "Valise," in the language developed to describe the associated Adinkras [6,8,12,14,15], indicates that all the bosons possess the same engineering units, and similarly all the fermions, offset by direct calculation on all the fields in the multiplet implies that (1.1b) are satisfied; each index I, J, . .…”

Nonlinear (4,8,4) multiplet of N=8

“…Some other multiplets of N =8, d=1 supersymmetry, e.g. (8,8,0) and (7,8,1) [17], also admit a description as constrained bi-harmonic analytic superfields [20]. So one can hope to find out nonlinear analogs of these multiplets, following the lines of this paper.…”