Symmetries of N=4 supersymmetric CP(n) mechanics

TL;DR

This paper constructs explicit symmetry generators for N=4 supersymmetric $ ext{CP}^n$ mechanics, revealing the Hamiltonian's structure as a sum of Casimir operators on $SU(n+1)$ and $SU(1,n)$ groups, highlighting underlying symmetries.

Contribution

It explicitly constructs the $SU(n+1)$ symmetry generators commuting with supercharges in N=4 supersymmetric $ ext{CP}^n$ mechanics with background gauge fields.

Findings

Hamiltonian expressed as sum of two Casimir operators.

Explicit form of $SU(n+1)$ symmetry generators.

Identification of isospin degrees of freedom in Hamiltonian.

Abstract

We explicitly constructed the generators of $SU(n+1)$ group which commute with the supercharges of N=4 supersymmetric $\mathbb{CP}^n$ mechanics in the background U(n) gauge fields. The corresponding Hamiltonian can be represented as a direct sum of two Casimir operators: one Casimir operator on $SU(n+1)$ group contains our bosonic and fermionic coordinates and momenta, while the second one, on the SU(1,n) group, is constructed from isospin degrees of freedom only.