Response of Kaluza-Klein mass spectrum to deformations of rugby-ball compact space

We investigate the response of the Kaluza-Klein (KK) mass spectrum to various deformations of the rugby-ball background in 6-dimensional supergravity. We derived the mode equations that contain the 3-dimensional scale factor and the lapse function. By solving these, we numerically evaluate the KK masses for a bulk scalar and a spinor when the background has a nontrivial dependence on the position in the compact space. We clarify some qualitative features of the spectrum deformation for some perturbations of the rugby-ball background. For perturbations of a supersymmetric background, we find that the mass-splitting between bosonic and fermionic modes is much smaller than the deviation from the values of the supersymmetric mass eigenvalues.