Naturalness and UV sensitivity in Kaluza-Klein theories
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More than twenty years ago a paradigm emerged according to which a UV-insensitive Higgs mass ${m}_{H}$ and (more generally) a UV-insensitive Higgs effective potential ${V}_{1l}(\ensuremath{\phi})$ are obtained from higher-dimensional theories with compact extra dimensions and Scherk-Schwarz supersymmetry breaking. Since then, these ideas have been applied to different models of phenomenological interest, including recent applications to the dark energy problem. A thorough analysis of the framework on which such a paradigm is based allows us to show that a source of strong UV sensitivity for ${m}_{H}$ and ${V}_{1l}(\ensuremath{\phi})$, intimately connected to the nontrivial topology of these models' spacetime, was missed. The usual picture of the Scherk-Schwarz mechanism and its physical consequences need to be seriously reconsidered.Keywords:
Kaluza–Klein theory
We investigate the microphysics of cosmic strings in non-Abelian gauge theories with $N=1$ supersymmetry. We give the vortex solutions in a specific example and demonstrate that fermionic superconductivity arises because of the couplings and interactions dictated by supersymmetry. We then use supersymmetry transformations to obtain the relevant fermionic zero modes and investigate the role of soft supersymmetry breaking on the existence and properties of the superconducting strings.
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Supersymmetry plays a main role in all current thinking about superstring theory. Indeed, many remarkable properties of string theory have been explained using supersymmetry as a tool. So far, there has been no unbroken supersymmetry observed in nature, and if nature is described by supersymmetry, it must be broken. Supersymmetry may be broken spontaneously at any order of perturbation theory or dynamically due to nonperturbative effects. To examine the methods of supersymmetry breaking, special attention is given to discuss the normalization of the ground state of the supersymmetric harmonic oscillator. This study explains that perturbation theory gives incorrect results for both the ground-state wave function and the energy spectrum and it fails to give an explanation to the supersymmetry breaking.
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Supersymmetry plays a main role in all current thinking about superstring theory.Indeed, many remarkable properties of string theory have been explained using supersymmetry as a tool.So far, there has been no unbroken supersymmetry observed in nature, and if nature is described by supersymmetry, it must be broken.Supersymmetry may be broken spontaneously at any order of perturbation theory or dynamically due to nonperturbative effects.To examine the methods of supersymmetry breaking, special attention is given to discuss the normalization of the ground state of the supersymmetric harmonic oscillator.This study explains that perturbation theory gives incorrect results for both the ground-state wave function and the energy spectrum and it fails to give an explanation to the supersymmetry breaking.
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In this short introduction to Kaluza-Klein (KK) theories, we emphasize on the possibility to obtain gauge fields from pure Einstein gravity in higher dimensions, a possibility introduced by Nordstrom (1914), Kaluza (1919), and Klein (1926). The original idea to introduce one extra space dimension to obtain electromagnetism and gravity in four dimensions offers a way to unify the two known forces of the 19th century and give them a common, geometrical origin. This idea is then taken further to show that non-Abelian gauge fields can be obtained, corresponding to the weak and strong forces, by introducing more spatial dimensions. A modern kind of Kaluza-Klein theory is represented by the theory of a universal extra dimension (UED), which can be seen as a generalization of the standard model of particle physics to five dimensions. It is shown that the four dimensional theory, as we observe it today, can be obtained, but with an extended particle spectrum that should be detectable at higher energies, depending on the size of the extra dimension. This work is part of a seminar course in theoretical physics given at KTH autumn 2005.
Kaluza–Klein theory
Universal extra dimension
Electromagnetism
Unified field theory
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Supersymmetry plays a main role in all current thinking about superstring theory. Indeed, many remarkable properties of string theory have been explained using supersymmetry as a tool. So far, there has been no unbroken supersymmetry observed in nature, and if nature is described by supersymmetry, it must be broken. Supersymmetry may be broken spontaneously at any order of perturbation theory or dynamically due to nonperturbative effects. To examine the methods of supersymmetry breaking, special attention is given to discuss the normalization of the ground state of the supersymmetric harmonic oscillator. This study explains that perturbation theory gives incorrect results for both the ground-state wave function and the energy spectrum and it fails to give an explanation to the supersymmetry breaking.
Normalization
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I provide a pedagogical introduction to supersymmetry.The level of discussion is aimed at readers who are familiar with the Standard Model and quantum field theory, but who have had little or no prior exposure to supersymmetry.Topics covered include: motivations for supersymmetry, the construction of supersymmetric Lagrangians, superspace and superfields, soft supersymmetry-breaking interactions, the Minimal Supersymmetric Standard Model (MSSM), R-parity and its consequences, the origins of supersymmetry breaking, the mass spectrum of the MSSM, decays of supersymmetric particles, experimental signals for supersymmetry, and some extensions of the minimal framework. Contents"We are, I think, in the right Road of Improvement, for we are making Experiments."-Benjamin Franklin § The parameter called b here is often seen elsewhere as Bµ or m 2 12 or m 2 3 .
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