The common origin of linear and nonlinear chiral multiplets in mechanics

Abstract

Elaborating on previous work (hep-th/0605211, 0611247), we show how the linear and nonlinear chiral multiplets of N =4 supersymmetric mechanics with the off-shell content (2,4,2) can be obtained by gauging three distinct two-parameter isometries of the "root" (4,4,0) multiplet actions. In particular, two different gauge groups, one abelian and one non-abelian, lead, albeit in a disguised form in the second case, to the same (unique) nonlinear chiral multiplet. This provides an evidence that no other nonlinear chiral N =4 multiplets exist. General sigma model type actions are discussed, together with the restricted potential terms coming from the Fayet-Iliopoulos terms associated with abelian gauge superfields. As in our previous work, we use the manifestly supersymmetric language of N =4, d=1 harmonic superspace. A novel point is the necessity to use in parallel the λ and τ gauge frames, with the "bridges" between these two frames playing a crucial role. It is the N =4 harmonic analyticity which, though being non-manifest in the τ frame, gives rise to both linear and nonlinear chirality constraints.

Superfield formulation of nonlinearN=4supermultiplets

“…Moreover, no other solutions exist within our approach. This is in full agreement with the claim of the paper [11] that all possible two-dimensional supermultiplets include chiral and nonlinear chiral supermultiplets only.…”

${\mathcal N} = 4$ SUPERSYMMETRIC QUANTUM MECHANICS AND HARMONICS

“…I am grateful to my co-authors in [3,[9][10][11][12][13][14][15], Francois Delduc, Sergey Fedoruk, Maxim Konyushikhin, Olaf Lechtenfeld and Andrei Smilga, for the successful collaboration. A partial support from the RFBR grants Nr.…”

“…These multiplets and their superfield actions can be reproduced via the appropriate gaugings of the multiplet (4, 4, 0) and of some nonlinear generalizations of the latter [9][10][11]:…”

“…• It allows one to understand an interplay between various N = 4 SQM models within the N = 4, d = 1 covariant gauging procedure [9][10][11]; • In its framework it becomes possible to set up generic N = 4, d = 1 superfield actions of the linear and nonlinear (4, 4, 0) multiplets [12]; • It allows one to find out new N = 4 superextensions of Calogero-type models [13]; • Using the HSS approach, new off-shell SQM models with the Lorentz-force-type couplings to the external nonabelian gauge fields were constructed in [14,15]. The basic idea of this construction consists in employing the spin (or semi-dynamical ) (4, 4, 0) multiplet.…”

SU (2|1) mechanics and harmonic superspace

“…As was argued in [8] in the component approach and in [9] in the superfield language, the basic multiplet of N = 4, d = 1 supersymmetry is the so called "root" multiplet (4,4,0). All other multiplets and the SQM models associated with them can be obtained from the root multiplet and the associate SQM models by some well-defined procedures: either by a sort of Hamiltonian reduction with respect to some isometries of the on-shell (4, 4, 0) Lagrangians, or by gauging these isometries in the off-shell superfield approach [9,10,11]. The natural superfield description of the multiplet (4, 4, 0), as well as of another important multiplet (3,4,1), is achieved in the framework of the harmonic N = 4, d = 1 superspace [12].…”