The Dark Sector and the Standard Model from a Local Generalisation of Extra Dimensions

Many models with structures of matter associated with a structure of extra spatial dimensions have been proposed in recent decades. On employing a further generalisation from the local 4-dimensional spacetime form to a general form for proper time, we describe how matter fields resembling the Standard Model of particle physics can be accommodated far more directly than with a higher-dimensional spacetime theory. The successful identification of key features of visible matter in this non-spatial sector of extra dimensions in turn motivates seeking a candidate for dark matter residing in the original extra spatial dimension sector, and provides a close guide for the explicit form this invisible matter might take. We describe how such Standard Model and dark matter sectors in different extra-dimensional branches of generalised proper time are gravitationally connected through their common root in the local 4-dimensional spacetime and consider further possible mutual interactions and implications in comparison with existing dark matter models. A yet further possible branch of generalised proper time can be connected with dark energy models, hence in principle accounting for all three major components of cosmological structure within this framework.

Quantum theory without classical time: Octonions, and a theoretical derivation of the Fine Structure Constant 1/137

There must exist a reformulation of quantum field theory which does not refer to classical time. We propose a pre-quantum, pre-spacetime theory, which is a matrix-valued Lagrangian dynamics for gravity, Yang–Mills fields, and fermions. The definition of spin in this theory leads us to an eight-dimensional octonionic spacetime. The algebra of the octonions reveals the standard model; model parameters are determined by roots of the cubic characteristic equation of the exceptional Jordan algebra. We derive the asymptotic low-energy value 1/137 of the fine structure constant, and predict the existence of universally interacting spin one Lorentz bosons, which replace the hypothesised graviton. Gravity is not to be quantized, but is an emergent four-dimensional classical phenomenon, precipitated by the spontaneous localisation of highly entangled fermions.

Quantum Theory Without Classical Time: Octonions, and a Theoretical Derivation of the Fine Structure Constant 1/137

There must exist a reformulation of quantum field theory which does not refer to classical time. We propose a pre-quantum, pre-spacetime theory, which is a matrix-valued Lagrangian dynamics for gravity, Yang-Mills fields, and fermions. The definition of spin in this theory leads us to an eight dimensional octonionic space-time. The algebra of the octonions reveals the standard model; model parameters are determined by roots of the cubic characteristic equation of the exceptional Jordan algebra. We derive the asymptotic low energy value 1/137 of the fine structure constant, and predict the existence of universally interacting spin one Lorentz bosons, which replace the hypothesised graviton. Gravity is not to be quantized, but is an emergent four-dimensional classical phenomenon, precipitated by the spontaneous localisation of highly entangled fermions.

$$ \frac{\mathrm{SL}\left(2,\mathrm{\mathbb{R}}\right)\times \mathrm{U}(1)}{\mathrm{U}(1)} $$ CFT, NS5+F1 system and single trace $$ T\overline{T} $$

In this paper we prove the equivalence among (i) the weakly coupled worldsheet string theory described by the coset sigma model $$ \frac{\mathrm{SL}{\left(2,\mathrm{\mathbb{R}}\right)}_k\times \mathrm{U}(1)}{\mathrm{U}(1)} $$ SL 2 ℝ k × U 1 U 1 × S3 × T4 with SL(2, ℝ) WZW level k ≥ 2, (ii) the full near horizon theory of the NS5 branes with k NS5 branes wrapping T4 × S1, p » 1 F1 strings wrapping S1 and n units of momentum along the S1 and (iii) the single trace $$ T\overline{T} $$ T T ¯ deformation of string theory in AdS3 × S3 × T4. As a check we compute the spectrum (continuous) of the spacetime theory by performing BRST quantization of the coset description of the worldsheet theory and show that it matches exactly with the one derived in the case of single trace $$ T\overline{T} $$ T T ¯ deformed string theory in AdS3. Secondly, we compute the two-point correlation function of local operators of the spacetime theory using the worldsheet coset approach and reproduce the same two-point function from the supergravity approach.

Platonic Quantum Set Theory Proposal and Fractal-Cantorian Heterotic Kaluza- Klein Spacetime

The four basic building blocks of the cosmos hypothesized by the Athenian philosopher Plato and his corresponding theory are replaced by the backbone golden mean based scaling pertinent to each of the four kinds of blocks. In the course of doing this we stretch and generalize Plato’s philosophical ideas to ultimately find out that it is essentially the deep philosophical origin of the golden mean number system of E-infinity Cantorian spacetime theory of high energy physics and quantum cosmology. Subsequently we use this new platonic form of E-infinity quantum set theory to uncover a remarkably rich Kaluza-Klein fractal version of Gross et al’s ingenious Heterotic superstring theory.

Spacetime

Spacetime is the four-dimensional manifold proposed by current physics as the arena for Nature’s show. Although Newtonian physics can very well be reformulated in a spacetime setting, the idea of spacetime was not developed until the twentieth century, in connection with Einstein’s theories of special and general relativity. Due to the success of special relativity in microphysics and of general relativity in astronomy and cosmology, every advanced physical theory is now a spacetime theory. Spacetime is undoubtedly an artificial concept, which our hominid ancestors did not possess, but the same is true of Newtonian space and time.

Unified DE–DM with diffusive interactions scenario from scalar fields

Generalized models of unified dark matter (DM) and dark energy (DE) in the context of Two Measure Theories and of dynamical spacetime theories are obtained. In Two Measure Theories, one uses metric independent volume elements and this allows to construct unified DM and DE, where the cosmological constant appears as an integration constant associated to the equation of motion of the measure fields. The dynamical spacetime theories generalize the Two Measure Theories by introducing a vector field whose equation of motion guarantees the conservation of a certain energy–momentum tensor, which may be related, but in general is not the same as the gravitational energy–momentum tensor. By considering the dynamical space field appearing in another part of the action (apart from the coupling to the energy–momentum tensor), we can obtain noncovariant energy–momentum conservation. Then, the dynamical spacetime theory becomes a theory of diffusive unified DE and DM. The nonconserved energy–momentum tensors lead at the end to a formulation of interacting DE–DM models in the form of a diffusive type interacting unified DE and DM scenario. We solved analytically the theories for asymptotic solution, and we show that the [Formula: see text]CDM is a fixed point of these theories at large times.

Unified scenario of three types of neutrinos with respective mass scales

A unified theory of three different types of neutrinos is discussed in the Kaluza–Klein (KK) five-dimensional spacetime theory. In particular, we construct the scenario in which the zeroth KK modes correspond to the left-handed neutrinos with the meV mass and the right-handed sterile neutrinos with the keV mass, whereas the first KK modes to the neutrinos with the TeV mass.