Geometric $\sigma$-models have been defined as purely geometric theories of scalar fields coupled to gravity. By construction, these theories possess arbitrarily chosen vacuum solutions. Using this fact, one can build a Kaluza--Klein geometric $\sigma$-model by specifying the vacuum metric of the form $M^4\times B^d$. The obtained higher dimensional theory has vanishing cosmological constant but fails to give massless gauge fields after the dimensional reduction. In this paper, a modified geometric $\sigma$-model is suggested, which solves the above problem.
展开▼
机译：几何σ模型已定义为与重力耦合的标量场的纯粹几何理论。通过构建，这些理论拥有任意选择的真空解决方案。利用这一事实，可以通过指定形式为$ M ^ 4 \ x B ^ d $的真空度量来构建Kaluza-Klein几何$ \ sigma $模型。所获得的高维理论具有消失的宇宙常数，但在维数减小后未能给出无质量的标称场。本文提出了一种改进的几何$ \ sigma $模型，可以解决上述问题。
展开▼
