A note on $SU(1,1|n)$ and $OSp(6|2)$ superconformal mechanics

TL;DR

This paper constructs superconformal mechanics models with $SU(1,1|n)$ and $OSp(6|2)$ symmetries, involving non-Abelian currents, and discusses algebraic constraints and solution methods for these models.

Contribution

It introduces new superconformal mechanics models with specific symmetry groups and explores algebraic equations governing their currents, providing explicit solutions in certain cases.

Findings

Currents expressed via semi-dynamical variables and coordinates.

Algebraic equations constrain currents for $N>4$ supersymmetries.

Methods for solving these algebraic equations are discussed.

Abstract

In this article we consider the construction of the superconformal mechanics that realize $SU(1,1|n)$ and $OSp(6|2)$ symmetries and involve interactions with non-Abelian bosonic currents. If is shown that for $N>4$ supersymmetries the currents involved have to satisfy the algebraic equations. General considerations on methods of solving these equations are given. In the obtained particular solutions currents are expressed in terms of semi-dynamical variables (harmonics), and, on one instance, coordinates and momenta.