The masses of bosonic particles in the fluctuating squashed 7-sphere

A detailed calculation of the spectrum of the lowest energy, E0, is presented for vector, axial vector, tensor, and scalar fluctuation modes (still incomplete) in eleven-dimensional supergravity compactified on the squashed 7-sphere. The general correspondence is also given between the generalised Laplacian and the quadratic G-Casimir invariant in an arbitrary homogeneous space G/H.