The Common Origin of Linear and Nonlinear Chiral Multiplets in N=4 Mechanics

TL;DR

This paper demonstrates that linear and nonlinear chiral multiplets in N=4 supersymmetric mechanics originate from gauging specific isometries of a root multiplet, revealing their fundamental connection and uniqueness.

Contribution

It shows how different gauge groups produce the same nonlinear chiral multiplet, providing evidence that no other such multiplets exist in N=4 mechanics.

Findings

Different gauge groups lead to the same nonlinear chiral multiplet.

The construction uses harmonic superspace with b1 and cb4 frames.

The work confirms the uniqueness of nonlinear chiral multiplets in this context.

Abstract

Elaborating on previous work (hep-th/0605211, hep-th/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 \lambda and \tau 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 \tau frame, gives rise to both linear and nonlinear chirality constraints.