2D Random Walks of Massless Higgs Bosons as Microscopic Interpretation of the Asymptotic Safety of Gravity, and of the Standard Model
Authors: Maes Stephane 
Published: January 2024

Renormalization, or asymptotic safety, of QFTs, and other models, are mathematical techniques to ensure not only the absence of divergences and regularity of the models, but also suitable stabilized UV and IR behaviors. In general, there are not always clear microscopic interpretations of what leads to renormalizability, or asymptotic safety, other than very often identifying some conformant symmetries, and, in particular, that the models are, or converge, towards CFTs, say based on dimensional analysis, or, for example, relying on effects like vacuum polarization as interpretation, or extended entities in the case of superstrings. In this paper, and based on the multi-fold theory, we give a physical interpretation to renormalization and asymptotic safety as the result of 2D random walks of particles, 2D Physics, multi-fold emergence of gravity effects, and multi-fold 7D space time matter induction and scattering of solitons in condensate Qballs, or in random walk patterns: at spatial scales below the multi-fold gravity electroweak symmetry breaking scales, i.e. at high energies, massless Higgs bosons are (roughly) free massless bosons propagating as CFTs, or dilatons, just as in JT or Liouville gravity, the latter being a CFT version of Einstein gravity in 2D, which is renormalizable.At spatial scales below the gravity electroweak symmetry breaking scales, per the multi-fold 7D induction and scattering, particles, bosons and fermions, are in random walks, following soliton patterns, or condensating in soliton Qballs, if existing as massive fluctuations. They are not point particles. Within and outside the solitons or patterns, charges/colors, resulting from the symmetries of the solitons, fade away, so that fields and matter couplings are tamed and constant: everything becomes CFTs. Therefore, gravity remains asymptotically safe in the presence of the Standard Model (SM). And it is really gravity based on General relativity (GR), and the SM, i.e., Yang Mills and Maxwell theories, which are asymptotically safe, something confirmed by all their 2D versions (JT/Liouville 2D dilaton gravity, 2D QED and 2D QCD). It microscopically motivates these interactions, including 2D gravity, and why the Ultimate Unification (UU) reigns, as only “unification”, and how the SM is an effective theory. Overall, only 2D physics matters! It also show that our universe must be closed.The paper argues that the embedding 7D is built by massless Higgs, which provides microscopic interpretations and motivation for multiple properties of multi-fold, previously introduced as principles, as well as why GR reigns in the 7D spacetime, and spacetime induction works. In fact, we confirm this by explaining how non-commutative spacetime can recover the SM and neutrino mixing via algebra doubling.With random walks with foraging and non-Markovian behaviors, as expected per the multi-fold spacetime reconstruction, we can explain inflation, expansion of spacetime, a complex/imaginary Higgs field pre electroweak symmetry breaking, and we can guarantee unitarity of Physics, even if it may sometimes statistically appear rather non-unitary, but Hermitian or isometric, or with non-Hermitian pseudo Hamiltonians, especially in an universe with a strictly positive cosmological constant.