Supermetrics on supermanifolds

Abstract

By virtue of the well-known theorem, a structure Lie group K of a principal bundle $P$ is reducible to its closed subgroup H iff there exists a global section of the quotient bundle P/K. In gauge theory, such sections are treated as Higgs fields, exemplified by pseudo-Riemannian metrics on a base manifold of P. Under some conditions, this theorem is extended to principal superbundles in the category of G-supermanifolds. Given a G-supermanifold M and a graded frame superbundle over M with a structure general linear supergroup, a reduction of this structure supergroup to an orthgonal-symplectic supersubgroup is associated to a supermetric on a G-supermanifold M.

17 pages

References in corpus (3)

• Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles
• Super coset space geometry
• Classical gauge theory of gravity

Cited by in corpus (6)

• Products in the category of ${\mathbb{Z}}_2^n$-manifolds
• Lectures on supergeometry
• Hidden Supersymmetry in Dirac Fermion Quasinormal Modes of Black Holes
• Higgs fields induced by Yang--Mills type Lagrangians on gauge-natural prolongations of principal bundles
• Supersymmetric sigma models and harmonic superfunctions
• Lecture on Gauge Gravitation Theory. Gravity as a Higgs Field