ORTHOSUPERSYMMETRIC QUANTUM MECHANICS

We construct a new form of supersymmetric quantum mechanics named orthosupersymmetric quantum mechanics. We show that there are p orthosupercharges Qα (α= 1,2, …, p) which satisfy the algebra [Formula: see text] where H is the Hamiltonian. The spectra of this class of systems are shown to be (p+1)-fold degenerate, at least above the ground state. We also discuss a model of conformal orthosupersymmetry of degree p and show that in this case there are p orthosupercharges, and p conformal orthosupercharges which along with H, dilatation generator D and conformal generator K form a closed algebra. A comparative discussion on parasupersymmetric and orthosupersymmetric quantum mechanics is also given.

SEARCH FOR EXTENDED CONFORMAL ALGEBRA

We search for the extended conformal algebra with two spin-s (s: integer) and one spin-1 generators. This search is inspired by the existence of chiral algebra in the Gaussian model for rational radius. For odd s, the conformal properties of the three-point functions imply that a general fusion rule can be reduced to those of the Gaussian model. For arbitrary even s, these conditions are weaker. In particular, for s=2 we show that the chiral algebra of the Gaussian model is the unique extended conformal algebra with the value of the central charge fixed to be c=1. It is also shown that the conformal generator is necessarily a bilinear of the spin-1 generator just as the Gaussian model. We conjecture that this remains true for arbitrary value of s.