Conformal Orthosymplectic Quantum Mechanics

TL;DR

This paper explores the curvature-related obstructions to symmetries in supersymmetric quantum mechanical models, revealing enhanced orthosymplectic symmetries in specific geometric settings and discussing potential generalizations.

Contribution

It identifies the most general curvature obstruction to certain symmetries and shows how these symmetries are enhanced under specific geometric conditions, introducing new conformal symmetries.

Findings

Curvature obstructs certain symmetry subalgebras.

Enhanced orthosymplectic symmetry in geometries with specific conformal Killing vectors.

Potential generalizations to three dimensions and Chern--Simons-like models.

Abstract

We present the most general curvature obstruction to the deformed parabolic orthosymplectic symmetry subalgebra of the supersymmetric quantum mechanical models recently developed to describe Lichnerowicz wave operators acting on arbitrary tensors and spinors. For geometries possessing a hypersurface-orthogonal homothetic conformal Killing vector we show that the parabolic subalgebra is enhanced to a (curvature-obstructed) orthosymplectic algebra. The new symmetries correspond to time-dependent conformal symmetries of the underlying particle model. We also comment on generalizations germane to three dimensions and new Chern--Simons-like particle models.