Kaluza–Klein tower and bubble nucleation in six dimensional Einstein–Maxwell theory

Abstract

AbstractWe study the implication of the distance and the cobordism conjecture on the 6-dimensional Einstein–Maxwell theory compactified on $$S^2$$ S 2 . In this toy model, the radion potential is stabilized by the conspiracy of the curvature of $$S^2$$ S 2 and the flux through $$S^2$$ S 2 parametrized by f, and uplifted by the positive 6-dimensional cosmological constant parametrized by $$\lambda $$ λ . When $$\lambda =0$$ λ = 0 , the radion is stabilized at the anti-de Sitter (AdS) vacuum, which cannot be interpolated to the Minkowski vacuum since the Kaluza–Klein (KK) tower descends from UV in the vanishing limit of the 4-dimensional cosmological constant. For nonzero $$\lambda $$ λ which realizes the metastable de Sitter (dS) vacuum, as well as the AdS and the Minkowski vacuum, such an obstruction can be found provided the combination $$f^2\lambda $$ f 2 λ is fixed and the limit $$\lambda \rightarrow 0$$ λ → 0 is taken. Moreover, the 6-dimensional Einstein–Maxwell theory allows the transition between vacua through the nucleation of the bubble. In this case, the values of the 4-dimensional cosmological constant inside and outside the bubble are different as f is changed at the bubble wall, while $$\lambda $$ λ remains unchanged. Regarding the AdS vacuum with the vanishing curvature radius as the ‘nothing’, we find that the transition from the metastable dS vacuum to the nothing is not prevented by the descent of the KK tower since $$f^2\lambda $$ f 2 λ is not fixed.