New variant ofN= 4 superconformal mechanics

Abstract

Proceeding from a nonlinear realization of the most general N =4, d=1 superconformal symmetry, associated with the supergroup D(2, 1; α), we construct a new model of nonrelativistic N =4 superconformal mechanics. In the bosonic sector it combines the worldline dilaton with the fields parametrizing the R-symmetry coset S 2 ∼ SU (2)/U (1). We present invariant off-shell N =4 and N =2 superfield actions for this system and show the existence of an independent N =4 superconformal invariant which extends the dilaton potential. The extended supersymmetry requires this potential to be accompanied by a d=1 WZW term on S 2 . We study the classical dynamics of the bosonic action and the geometry of its sigma-model part. It turns out that the relevant target space is a cone over S 2 for any non-zero α = ± 1 2 . The constructed model is expected to be related to the 'relativistic' N =4 mechanics of the AdS 2 × S 2 superparticle via a nonlinear transformation of the fields and the time variable.

Hierarchy of mechanics models

“…Therefore, some of N=8 mechanics models are dimensional reductions of N=2 super Yang-Mills theory or models of self-interacting N=2 hypermultiplets in four dimensions. The d=1 reduction of the gauge multiplet can yield either one of the off-shell N=8 multiplets (5,8,3) and (2,8,6) (in the classification of refs. [10,20] 1 ), depending on whether one performs the reduction on the level of the gauge potential superfield [21]- [24] or the superfield strength [25]- [27].…”

“…The d=1 reduction of the generic hypermultiplet model (which exists off shell only in harmonic superspace [28,29]) produces a general one-dimensional sigma model with hyperkähler target geometry and an infinite number of auxiliary fields. Finally, the d=1 reduction of the general off-shell sigma model for twisted N=(4, 4) supermultiplets in two dimensions leads to the most general model of the N=8 multiplet (4,8,4) [30,31].…”

“…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.…”

“…Later on, some of these multiplets (as well as their nonlinear cousins) and associated N=8 mechanics were studied in more detail in [25,26,27,30] and [34]- [40]. The general sigma-model type action for the multiplet (5,8,3), both in N=4 superfield formulation and in N=8 harmonic superfield formulation, had been constructed earlier in [21]- [24]. Superconformally invariant actions for the multiplets (3,8,5) and (5,8,3), in N=4 superfield formulation, were given in [10].…”

“…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).…”