A super vielbein is the analogue of a vielbein in supergeometry.
Let $N$ be a real spin representation and let $(x^a, \theta^\alpha)$ be the canonical coordinates on the supermanifold $\mathbb{R}^{d-1,1\vert N}$ underlying the super Minkowski spacetime super translation group. Then the canonical super vielbein is the $\mathbb{R}^{d-1,1\vert N}$-valued super differential form with components
$\psi^\alpha \coloneqq \mathbf{d} \theta^\alpha$.
$e^a \coloneqq \mathbf{d} x^a + \overline{\theta} \Gamma^a \mathbf{d} \theta$.
For more see at geometry of physics – supersymmetry.
Last revised on January 23, 2020 at 05:59:02. See the history of this page for a list of all contributions to it.