Improvement of a provisional solution of the quantum-corrected field equations of d = 11 supergravity on flat R^4 times a compact hyperbolic 7-manifold, and modes that decay along the beam line outside the interaction region at the LHC

Abstract

A recent provisional solution of the quantum-corrected field equations of d = 11 supergravity on flat R^4 times a compact hyperbolic 7-manifold \bar{H}^7, in the presence of magnetic 4-form fluxes wrapping 4-cycles of \bar{H}^7, is improved by showing that the curvature radius B of \bar{H}^7 and the r.m.s. 4-form flux strength h each have a single stationary point as the field redefinition parameter c is varied. Application of the principle of minimal sensitivity then fixes c in a moderate range such that B and h^{1/3} vary by only 4% and 5% respectively over this range. The new best value of B is 0.28 κ_{11}^{2/9} = 1.2 M_{11}^{-1}. The low-lying bosonic Kaluza-Klein modes of the bulk are studied. The classically massless harmonic 3-form modes of the 3-form gauge field, whose number is estimated as roughly 10^{32} if the intrinsic volume of \bar{H}^7 is ~ 10^{35}, acquire a mass 0.2 A/B from quantum corrections, where the warp factor A is fixed by the boundary conditions at the Horava-Witten (HW) boundary to lie between about 0.7 and 0.9. They have axion-like couplings to the SM gauge bosons. Their lifetimes range from about 10^{-27} seconds to several hours depending on the distance of their centre from the HW boundary, and they can decay along the beam line outside the interaction region at the LHC, with a distribution that shows a power law rather than exponential decrease with distance from the IP. Approximate exclusion limits are obtained from recent LHC data, and discovery prospects at ATLAS and CMS are studied.