New D(2,1;alpha) Mechanics with Spin Variables

TL;DR

This paper introduces a new superconformal mechanics model with D(2,1;alpha) symmetry, incorporating spin variables that form a fuzzy sphere upon quantization, and explores its algebraic structure and physical implications.

Contribution

It presents a novel superconformal mechanics model with spin variables, generalizing previous models and analyzing its algebraic and quantum properties.

Findings

Constructed classical and quantum generators of D(2,1;alpha)

Realized superalgebra on physical states with multiplets

Identified quantized conformal potential related to magnetic field

Abstract

We elaborate on a novel superconformal mechanics model possessing D(2,1;alpha) symmetry and involving extra U(2) spin variables. It is the one-particle case of the N=4 superconformal matrix model recently proposed in arXiv:0812.4276 [hep-th], and it generalizes to arbitrary alpha\neq0 the OSp(4|2) superconformal mechanics of arXiv:0905.4951 [hep-th]. As in the latter case, the U(2) spin variables are described by a Wess-Zumino action and define the first Hopf map S^3 -> S^2 in the target space. Upon quantization, they represent a fuzzy sphere. We find the classical and quantum generators of the D(2,1;alpha) superalgebra and their realization on the physical states. The super wavefunction encompasses various multiplets of the SU(2)_R and SU(2)_L subgroups of D(2,1;alpha), with fixed isospins. The conformal potential is determined by the external magnetic field in the Wess-Zumino term, whose amplitude is quantized like in the OSp(4|2) case. As a byproduct, we reveal new invariant subspaces in the enveloping algebra of D(2,1;alpha) for our quantum realization.