Supermetric

Supersymmetry gauge theory including supergravity is mainly developed as a Yang - Mills gauge theory with spontaneous breakdown of supersymmetries. There are various superextensions of pseudo-orthogonal Lie algebras and the Poincaré Lie algebra. The nonlinear realization of some Lie superalgebras have been studied. However, supergravity introduced in SUSY gauge theory has no geometric feature as a supermetric.

In gauge theory on a principal bundle ${\displaystyle P\to M}$ with a structure group ${\displaystyle K}$, spontaneous symmetry breaking is characterized as a reduction of ${\displaystyle K}$ to some closed subgroup ${\displaystyle H}$. By the well-known theorem, such a reduction takes place if and only if there exists a global section ${\displaystyle h}$ of the quotient bundle ${\displaystyle P/H\to M}$. This section is treated as a classical Higgs field.

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