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 ${\cal H}^{(2,2)}\times S^1$ 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 r\^ole 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 Schr\"odinger 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 $\rho\to0$ 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.
Highlights
The corresponding continuous spectrum of effective-theory massive states can prevent the effective localisation of lower-dimensional gravity, unless somehow a mass gap can be arranged below the edge of the continuous spectrum
This model has the unusual property of having a scalar field with a positive potential, as opposed to the negative or indefinite sign potentials arising in models with gauged compact symmetries
The link between the Salam-Sezgin model and supergravities related to string theory is given by its embedding into 10D type IIA supergravity by a lift on the noncompact space H(2,2) [13]
Summary
Consider gravitational fluctuations around the Salam-Sezgin background, considered from a braneworld four-dimensional perspective. General studies [7, 14] of the fluctuation problem about supergravity backgrounds start with an ansatz replacing the 4D metric ημν by ημν + hμν(x, z) where xμ are the 4D coordinates and zn = (y, ψ, θ, φ, χ, ρ) are the six “transverse” coordinates. One notes from the Salam-Sezgin background solution (2.9) that, of these, the five coordinates (y, ψ, θ, φ, χ) all refer to naturally compact directions, while ρ is the non-compact “radius”. Is the Salam-Sezgin warp function, (4) is the 4D d’Alembertian, y,ψ,θ,φ,χ is the Laplacian for the five compact directions (y, ψ, θ, φ, χ) (which will have zero eigenvalue for our S-wave treatment) and.
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