About the construction of p-adic QFT limit of TGD

Abstract

The p-adic description of Higgs mechanism provides excellent predictions for elementary particle and hadron masses. In this work the construction of p-adic field theory limit of Quantum TGD is considered. Topological condensate defined as a manifold obtained by gluing together p-adic spacetime regions with different values of $p$ is identified as 'quantum average' space time defined as absolute minimum of effective action $S_e$ associated with K\"ahler Dirac action defining configuration space geometry. p-Adic spacetime topology is ultrametric in accordance with the analogy with spin glass phase implied by the vacuum degenerary of K\"ahler action. Symmetry arguments suggest that $S_e$ in presence of fermion fields is just the super symmetrized K\"ahler Dirac action. Super symmetrization motivated by $N=1$ super symmetry generated by right handed neutrino replaces H-coordinates with their super counterparts and requires color singletness of physical states appears as consistency condition. p-Adic $Diff(M^4)$ and canonical transformations of $CP_2$ localized with respect to $M^4$ are approximate symmetries of the effective action and broken only by the nonflatness of the induced metric. Super gauge invariances in interior allow only massless many boson states with vanishing electroweak and color quantum numbers including graviton in accordance with the hypothesis that elementary particle quantum numbers reside on boundaries. Boundary components are idealized with world lines and Kac Moody Dirac spinors used in mass calculations describe the conformal degrees of freedom of the boundary component. Perturbation theory in powers of $p$ converges extremely rapidly: UV divergences are absent but natural infrared cutoff is present.