Braneworld localisation in hyperbolic spacetime

Abstract

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 hyperbolic ${\mathcal{H}}^{(2,2)}\times S^1$ 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 $V=-1/(4{\rho }^2)$ potential, where $\rho$ 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 $\rho \to 0$ 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.

32 pages, 2 figures; misprints corrected & some clarification added

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• Mass Gaps and Braneworlds -- In Memory of Peter Freund
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• Self-Tuning at Large (Distances): 4D Description of Runaway Dilaton Capture
• Covert Symmetry Breaking
• Cheeger bounds on spin-two fields
• Higgs Effect Without Lunch