Large star/rose extra dimension with small leaves/petals

In this paper, we propose to compactify a single Large Extra Dimension (LED) on a star/rose graph with a large number of identical leaves/petals. The 5D Planck scale can be chosen to be [Formula: see text] TeV which can provide a path to solve the gauge hierarchy problem. The leaf/petal length scale is of [Formula: see text], where [Formula: see text] GeV is the weak scale, without the large geometrical hierarchy of the traditional LED models to stabilize. The 4D fields of the SM are localized on a 3-brane at the central vertex of the star/rose graph. We predict a tower of feebly coupled weak scale Kaluza–Klein (KK) gravitons below a regime of strongly coupled gravitational phenomena above the TeV scale. Moreover, we reformulate in our setup the LED mechanism to generate light Dirac neutrinos, where the right-handed neutrinos are KK-modes of gauge singlet fermions propagating in the bulk. A large number of KK-gravitons and KK-neutrinos interact only gravitationally and thus constitute a hidden sector.

Supersymmetry, or the Defence of Scalars

The only fields of the Standard Model whose masses are not protected by a symmetry are the scalar fields. Supersymmetry is a symmetry between fermions and bosons which provides precisely such a protection mechanism. This chapter presents a comprehensive study of supersymmetric field theories. In particular, it is shown that they do not suffer from the phenomenon of gauge hierarchy. They have remarkable renormalisation properties and offer the most attractive framework to build a unified theory. The breaking of supersymmetry, both explicit and spontaneous, is studied in detail. The generalisation of electric-magnetic duality in supersymmetric theories yields non-perturbative results and the concept of twist makes possible the study of topological field theories. The supersymmetric extension of the Standard Model is shown to predict the existence of new elementary particles, whose phenomenological properties are analysed.

Hyperbolic deformation of a gauge field theory and the hierarchy problem

The problem of the gauge hierarchy is brought up in a hypercomplex scheme for a [Formula: see text] field theory; in such a scheme, a compact gauge group is deformed through a [Formula: see text]-parameter that varies along a noncompact internal direction, transverse to the [Formula: see text] compact one, and thus an additional [Formula: see text] gauge symmetry is incorporated. This transverse direction can be understood as an extra internal dimension, which will control the spontaneous symmetry breakdown, and will allow us to establish a mass hierarchy. In this mechanism, there is no brane separation to be estabilized as in the braneworld paradigm, however, a different kind of fine-tuning is needed in order to generate the wished electroweak/Planck hierarchy. By analyzing the effective self-interactions and mass terms of the theory, an interesting duality is revealed between the real and hybrid parts of the effective potential. This duality relates the weak and strong self-interaction regimes of the theory, due to the fact that both mass terms and self-coupling constants appear as one-parameter flows in [Formula: see text]. Additionally, the [Formula: see text]-deformation will establish a flow for the electromagnetic coupling that mimics the renormalization group flow for the charge in QED.

Classical conformality in the Standard Model from Coleman’s theory

The classical conformality (CC) is one of the possible candidates for explaining the gauge hierarchy of the Standard Model (SM). We show that it is naturally obtained from the Coleman’s theory on baby universe.

Off-shell supersymmetry

Supersymmetry does not dictate the way we should quantize the fields in the supermultiplets, and so we have the freedom to quantize the Standard Model (SM) particles and their superpartners differently. We propose a generalized quantization scheme under which a particle can only appear off-shell, while its contributions to quantum corrections are exactly the same as those in the usual quantum field theory. We apply this quantization scheme solely to the sparticles in the R-parity preserving Minimal Supersymmetric Standard Model (MSSM). Thus, sparticles can only appear off-shell. They could be light but would completely escape the direct detection at any experiments such as the LHC. However, our theory still retains the same desirable features of the usual MSSM at the quantum level. For instance, the gauge hierarchy problem is solved and the three MSSM gauge couplings are unified in the usual way. Although direct detection of sparticles is impossible, their existence can be revealed by precise measurements of some observables (such as the running QCD coupling) that may receive quantum corrections from them and have sizable deviations from the SM predictions. Also, the experimental constraints from the indirect sparticle search are still applicable.

Gauge hierarchy problem, supersymmetry, and fermionic symmetry

We reconsider the gauge hierarchy problem from the viewpoint of effective field theories and a high-energy physics, motivated by the alternative scenario that the standard model holds up to a high-energy scale such as the Planck scale. The problem is restated as the question whether it is possible to construct a low-energy effective theory and the interaction with heavy particles, without spoiling the structure of a high-energy physics supported by an excellent concept. Based on this reinterpretation, we give a conjecture that theories with hidden fermionic symmetries can be free from the gauge hierarchy problem and become candidates of the physics beyond and/or behind the standard model, and present toy models with particle-ghost symmetries as illustrative examples and a prototype model for the grand unification.