AP Theory II:Intrinsic 4D Quantum YM Theory with Mass Gap

TL;DR

This paper introduces a rigorous, non-perturbative sub-theory of Artin Presentation Theory that models key aspects of 4D Quantum Yang-Mills theory, including the mass gap, without relying on traditional quantum field theory constructs.

Contribution

It presents a novel, mathematically rigorous framework based on discrete group theory and holography that challenges the necessity of PDE-based quantum field theories for the YM problem.

Findings

Provides a discrete, group-theoretic analog of YM with a mass gap.

Develops a holographic principle that impacts the structure of 4D QFT.

Contains an analogue of Donaldson/Seiberg-Witten theory within a rigorous framework.

Abstract

We describe a sub-theory of Artin Presentation Theory (AP Theory), which has many genuine,discrete,group-theoretic,non-infinitesimal, qualitative analogues (including with the mass gap) of the main desiderata of the hypothetical quantitative infinitesimal '4D Quantum YM Theory' for the so-called Clay Millenium 'YM Existence and Mass Gap' problem. Our entirely mathematically rigorous theory is not a model, no new axioms or measures are introduced,does not rely on SUSY,is free of smooth 4D singularities,moduli spaces,path integrals, graph/lattice combinatorics and probabilistic,category,twistor or topos arguments and is intimately related to the theory of pure framed braids. Despite being based on a rigorous, radical,universal Holographic Principle,the theory still contains an analogue of Donaldson/Seiberg-Witten Theory, an infinitely generated, at each stage, graded group of topology-changing transitions and interactions and more. Our main contention is: the radical,universal AP-holography, with its strong topology changing interactions, which reach all the way to the 'vacuum' of discrete group theory, may destroy any infinitesimal, PDE based Field Theory,required for solving the actual Clay YM problem in its present quantitative form as a problem of so-called 'constructive' 3+1 QFT. More generally,due to the fact that AP Theory is not a model,e.g., does not introduce any new axioms,any rigorous axiomatic 3+1 QFT has to align itself with it in a mathematically rigorous fashion.