On Nonlinear σ-Models Arising in (Super-)Gravity

Abstract:

In a previous paper with Gibbons [1] we derived a list of three dimensional symmetric space σ-models obtained by dimensional reduction of a class of four dimensional gravity theories with abelian gauge fields and scalars. Here we give a detailed analysis of their group theoretical structure leading to an abstract parametrization in terms of “triangular” group elements. This allows for a uniform treatment of all these models. As an interesting application we give a simple derivation of a “Quadratic Mass Formula” for strictly stationary black holes.