Composite Supersymmetries in low-dimensional systems

TL;DR

This paper demonstrates how composite supermultiplets emerge from fundamental supersymmetric constituents in 2+1 dimensions and explores their implications for condensed matter systems like high-temperature superconductors.

Contribution

It explicitly constructs composite supermultiplets from fundamental ones and extends the supersymmetry algebra to include topological effects in low-dimensional systems.

Findings

Composite supermultiplets are formed from fundamental constituents.

Extension to N=2 superalgebra with central charge is achieved.

Relevance to infrared dynamics of high-temperature superconductors is discussed.

Abstract

Starting from a N=1 scalar supermultiplet in 2+1 dimensions, we demonstrate explicitly the appearance of induced N=1 vector and scalar supermultiplets of composite operators made out of the fundamental supersymmetric constituents. We discuss an extension to a N=2 superalgebra with central extension, due to the existence of topological currents in 2+1 dimensions. As a specific model we consider a supersymmetric $CP^1$ $\sigma$-model as the constituent theory, and discuss the relevance of these results for an effective description of the infrared dynamics of planar high-temperature superconducting condensed matter models with quasiparticle excitations near nodal points of their Fermi surface.