“Root” action forN=4supersymmetric mechanics theories

Abstract

We propose to consider the N = 4, d = 1 supermultiplet with (4, 4, 0) component content as a "root" one. We elaborate a new reduction scheme from the "root" multiplet to supermultiplets with a smaller number of physical bosons. Starting from the most general sigma-model type action for the "root" multiplet, we explicitly demonstrate that the actions for the rest of linear and nonlinear N = 4 supermultiplets can be easily obtained by reduction.Within the proposed reduction scheme there is a natural possibility to introduce Fayet-Iliopoulos terms. In the reduced systems, such terms give rise to potential terms, and in some cases also to terms describing the interaction with a magnetic field.We demonstrate that known N = 4 superconformal actions, together with their possible interactions, appear as results of the reduction from a free action for the "root" supermultiplet. As a byproduct, we also construct an N = 4 supersymmetric action for the linear (3, 4, 1) supermultiplet, containing both an interaction with a Dirac monopole and a harmonic oscillator-type potential, generalized for arbitrary conformally flat metrics.

A Journey Through Garden Algebras

“…The oxidation procedure is a nice tool that can be used to proceed in this way. Recently, exploiting the automorfic duality, it has been shown [23] that it is possible to relate not only the N = 4 root tree supermultiplets, but even the associated interacting sigma models 7 . Anyway, if we work outside the root tree, it is still not completely clear what kind of theories can be constructed with such supermultiplets.…”

Hierarchy of mechanics models

“…In this sense (2.38) is the true analog of the general sigma-model type action of the single "root" N=4 supermultiplet (4, 4, 0) [33]. Thus the class of general actions of two mutually "mirror" N=4 "root" multiplets (4, 4, 0) involves a subclass of N=8 supersymmetric actions.…”

“…We argue that the generic sigmamodel-type off-shell component action of each N=8 model (b, 8, 8−b) can be obtained from this (8,8,0) "parent" action via automorphic duality and demonstrate this property for b ≥ 5. This hierarchical structure of the N=8 mechanics models generalizes the N=4 hierarchy established in [33].…”

“…The restricted conformal factor will satisfy the dimension-7 harmonicity condition as a consequence of the dimension-8 equation (2.45). This consideration is the direct N=8 analog of a similar procedure in [33] where the general off-shell component action of the N=4 multiplet (3, 4, 1) was obtained from the general action of the "root" multiplet (4, 4, 0) . An essential difference is, however, that the conformal factors in the N=4 cases generally do not satisfy any harmonicity condition, while in the N=8 cases they necessarily do.…”

“…For instance, in the case of N=4 and N=8 supersymmetry there exist off-shell multiplets with field contents (4, 4, 0) and (8,8,0), respectively (so-called "root" [32,33] or "extreme" multiplets). These cannot be recovered by dimensional reduction because the suitable d>1 off-shell multiplets always include auxiliary fields.…”