Spectrum degeneracy and new symmetries for generalized Euler form actions

Abstract

Higher-dimensional gravity theories based on dimensionally continued Euler forms lead to a degenerate spectrum. It contains fewer excitations than the one of a genetic theory with arbitrary coefficients of the higher derivative terms. This can be traced back to a residual topological invariance of the action. The symmetry of the theory is enhanced. As a consequence the stability group of the vacuum can be larger than in the generic case. At the four-dimensional level this can even lead to infinite dimensional (Kac-Moody type) gauge algebras. A simple six-dimensional example leads to infinite towers of massless gravitons and scalars, but no spin-one bosons (gauge bosons) are present. We describe how modes decouple when the action approaches the Euler form. Concerning classical stability the Euler form corresponds to a singular point in the space of six-dimensional gravity actions.