Quantum SUSY Algebra of $Q$-lumps in the Massive Grassmannian Sigma Model

TL;DR

This paper derives the quantum supersymmetry algebra of $Q$-lumps in a massive Grassmannian sigma model in 2+1 dimensions, revealing the central extension structure through canonical quantization.

Contribution

It provides a detailed derivation of the quantum SUSY algebra for $Q$-lumps, including the central extension, using Scherk-Schwarz reduction and Dirac quantization methods.

Findings

Quantum SUSY algebra with central extension derived

Operator ordering affects algebra structure

Reproduction of classical action via dimensional reduction

Abstract

We compute the $\mathcal{N}=2$ SUSY algebra of the massive Grassmannian sigma model in 2+1 dimensions. We first rederive the action of the model by using the Scherk-Schwarz dimensional reduction from $\mathcal{N}=1$ theory in 3+1 dimensions. Then, we perform the canonical quantization by using the Dirac method. We find that a particular choice of the operator ordering yields the quantum SUSY algebra of the $Q$-lumps with cental extension.