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Register a new userCargese Lectures on Extra Dimensions
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R. Rattazzi
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I give a pedagogical introduction to the concepts and the tools that are necessary to study particle physics models in higher dimensions. I then give a more detailed presentation of warped compactifications and discuss their possible relevance to the hierarchy problem.
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These lectures give an introduction to the interrelated topics of Calabi-Yau compactification of the type II string, black hole attractors, the all-orders entropy formula, the dual (0,4) CFT, topological strings and the OSV conjecture. Based on notes by MG of lectures by AS at the 2006 Cargese summer school.
We review the six dimensional universal extra dimension models compactified on the sphere $S^2$, the orbifold $S^2/Z_2$, and the projective sphere, which are based on the spontaneous compactification mechanism on the sphere. In particular, we spell out the application of the Newman-Penrose eth-formalism on these models with some technical details on the derivation of the Kaluza-Klein modes and their interactions, and revisit the problem in the existence of the zero mode of $U(1)_X$ additional gauge boson required for the spontaneous compactification. We also explain the theoretical background on the vacuum stability argument for the upper bound on the ultraviolet cutoff scale.
We analyze the behaviour of the high-energy scattering amplitude within the brane world scenario in extra dimensions. We argue that contrary to the popular opinion based on the Kaluza-Klein approach, the cross-section does not increase with energy, but changes the slope close to the compactification scale and then decreases like in the 4-dimensional theory. A particular example of the quark-antiquark scattering due to the gluon exchange in the bulk is considered.
We reconsider cosmological constraints on extra dimension theories from the excess production of Kaluza-Klein gravitons. We point out that, if the normalcy temperature is above 1 GeV, then graviton states produced at this temperature will decay early enough that they do not affect the present day dark matter density, or the diffuse gamma ray background. We rederive the relevant cosmological constraints for this scenario.
We investigate preheating in a higher-dimensional generalized Kaluza-Klein theory with a quadratic inflaton potential $V(phi)=frac12 m^2phi^2$ including metric perturbations explicitly. The system we consider is the multi-field model where there exists a dilaton field $sigma$ which corresponds to the scale of compactifications and another scalar field $chi$ coupled to inflaton with the interaction $frac12 g^2phi^2chi^2+tilde{g}^2phi^3chi$. In the case of $tilde{g}=0$, we find that the perturbation of dilaton does not undergo parametric amplification while the $chi$ field fluctuation can be enhanced in the usual manner by parametric resonance. In the presence of the $tilde{g}^2phi^3chi$ coupling, the dilaton fluctuation in sub-Hubble scales is modestly amplified by the growth of metric perturbations for the large coupling $tilde{g}$. In super-Hubble scales, the enhancement of the dilaton fluctuation as well as metric perturbations is weak, taking into account the backreaction effect of created $chi$ particles. We argue that not only is it possible to predict the ordinary inflationary spectrum in large scales but extra dimensions can be held static during preheating in our scenario.
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