Narrow Results

In this paper, motivated by the recent discovery of a Higgs-like boson at the Large Hadron Collider (LHC) with a mass m_H≃125 GeV, we review different models where the hierarchy problem is solved by means of a warped extra dimension. In the Randall–Sundrum (RS) model electroweak observables provide very strong bounds on the mass of KK modes which motivates extensions to overcome this problem. Two extensions are briefly discussed. One particular extension is based on the deformation of the metric such that it strongly departs from the AdS₅ structure in the IR region while it goes asymptotically to AdS₅ in the UV brane. This model has the IR brane close to a naked metric singularity (which is outside the physical interval) characteristic of soft-walls constructions. The proximity of the singularity provides a strong wave function renormalization for the Higgs field which suppresses the T and S parameters. The second class of considered extensions are based on the introduction of an extra gauge group in the bulk such that the custodial SU(2)_R symmetry is gauged and protects the T parameter. By further enlarging the bulk gauge symmetry one can find models where the Higgs is identified with the fifth component of gauge fields and for which the Higgs potential along with the Higgs mass can be dynamically determined by the Coleman–Weinberg mechanism.

We analyze Ricci flow (normalized/unnormalized) of product manifolds — unwarped as well as warped, through a study of generic examples. First, we investigate such flows for the unwarped scenario with manifolds of the type 𝕊ⁿ × 𝕊^m, 𝕊ⁿ × ℍ^m, ℍ^m × ℍⁿ and also, similar multiple products. We are able to single out generic features such as singularity formation, isotropization at particular values of the flow parameter and evolution characteristics. Subsequently, motivated by warped braneworlds and extra dimensions, we look at Ricci flows of warped space–times. Here, we are able to find analytic solutions for a special case by variable separation. For others, we numerically solve the equations and draw certain useful inferences about the evolution of the warp factor, the scalar curvature as well as the occurrence of singularities at finite values of the flow parameter. We also investigate the dependence of the singularities of the flow on the initial conditions. We expect our results to be useful in any physical/mathematical context where such product manifolds may arise.