Hidden supersymmetry of a $P,T-$invariant $3D$ fermion system

TL;DR

This paper reveals a hidden supersymmetry in a (2+1)-dimensional P,T-invariant free fermion system, which leads to a superextension of the Poincaré group and impacts the representation of one-particle states.

Contribution

It uncovers a novel N=3 supersymmetry and a U(1,1) dynamical symmetry in a P,T-invariant fermion model relevant to high-Tc superconductivity.

Findings

Identification of a hidden N=3 supersymmetry.

Discovery of a superextension of the (2+1)D Poincaré group.

One-particle states form an irreducible supergroup representation.

Abstract

We show that a (2+1)-dimensional $P,T-$invariant free fermion system, relevant to $P,T-$conserving models of high-$T_c$ superconductivity, has a U(1,1) dynamical symmetry as well as an $N=3$ supersymmetry with the even generator being a quadratic function of the spin operator and of the generator of chiral ${\rm U_c(1)}$ transformations. We demonstrate that the hidden supersymmetry leads to a non-standard superextension of the (2+1)-dimensional Poincar\'e group. As a result, the one particle states of the $P,T-$invariant fermion system realize an irreducible representation of the Poincar\'e supergroup labelled by the zero eigenvalue of the superspin operator.