nLab super vielbein






A super vielbein is the analogue of a vielbein in supergeometry.

The canonical super vielbein

Let NN be a real spin representation and let (x a,θ α)(x^a, \theta^\alpha) be the canonical coordinates on the supermanifold d1,1|N\mathbb{R}^{d-1,1\vert N} underlying the super Minkowski spacetime super translation group. Then the canonical super vielbein is the d1,1|N\mathbb{R}^{d-1,1\vert N}-valued super differential form with components

  • ψ αdθ α\psi^\alpha \coloneqq \mathbf{d} \theta^\alpha.

  • e adx a+θ¯Γ adθe^a \coloneqq \mathbf{d} x^a + \overline{\theta} \Gamma^a \mathbf{d} \theta.

For more see at geometry of physics – supersymmetry.

Last revised on May 18, 2024 at 08:50:41. See the history of this page for a list of all contributions to it.