Braneworld localisation in hyperbolic spacetime

We present a construction employing a type IIA supergravity and 3-form flux background together with an NS5-brane that localises massless gravity near the 5-brane worldvolume. The nonsingular underlying type IIA solution is a lift to 10D of the vacuum solution of the 6D Salam-Sezgin model and has a hyperbolicH(2,2)×S1 structure in the lifting dimensions. A fully back-reacted solution including the NS5-brane is constructed by recognising the 10D Salam-Sezgin vacuum solution as a “brane resolved through transgression.” The background hyperbolic structure plays a key rôle in generating a mass gap in the spectrum of the transverse-space wave operator, which gives rise to the localisation of gravity on the 6D NS5-brane worldvolume, or, equally, in a further compactification to 4D. Also key to the successful localisation of gravity is the specific form of the corresponding transverse wavefunction Schrödinger problem, which asymptotically involves a V = −1/(4ρ2) potential, where ρ is the transverse-space radius, and for which the NS5-brane source gives rise to a specific choice of self-adjoint extension for the transverse wave operator. The corresponding boundary condition as ρ→ 0 ensures the masslessness of gravity in the effective braneworld theory. Above the mass gap, there is a continuum of massive states which give rise to small corrections to Newton’s law. email: [email protected] email: [email protected] email: [email protected] ar X iv :1 40 8. 70 72 v1 [ he pth ] 2 9 A ug 2 01 4