AP Theory III: Cone-like Graded SUSY, Dynamic Dark Energy and the YM Millenium Problem

TL;DR

This paper introduces AP Theory, a novel framework linking discrete group theory with smooth 4-manifolds, offering a non-perturbative, background-independent approach that addresses fundamental problems like dark energy and the YM mass gap.

Contribution

It presents AP Theory as a new, rigorous, topological approach unifying gauge-gravity duality, smooth topology change, and key physics problems within a discrete group-theoretic framework.

Findings

Establishes a gauge-theoretic model for smooth topology change.

Links the Cosmological Constant problem with the YM Mass Gap.

Proposes a non-perturbative, background-independent quantum gravity model.

Abstract

Artin Presentation Theory, (AP Theory), is a new, direct infusion, via pure braid theory, of discrete group theory, (i.e., symmetry in its purest form), into the theory of {\it smooth} 4-manifolds, (i.e.,$(3+1)$-Quantum Gravity in its purest topological form), thus exhibiting the most basic, rigorous, universal, model-free intrinsic {\it gauge-gravity} duality in a non-infinitesimal, cone-like graded, as holographic as possible, model-independent, non-perturbative, background-independent, parameter-free manner. {\it In AP Theory even smooth topology change becomes gauge-theoretic, setting the stage for a rigorous smooth topological $(3+1)$-QFT of Dynamic Dark Energy.} In this theory, the rigid $\infty$ of the dimension of classical Hilbert space is substituted by the dynamic $\infty$ of the $\infty$ generation at each stage of a cone-like graded subgroup of topology-changing transitions/interactions. As a corollary, the Cosmological Constant problem and the YM Millenium Mass Gap problem, two of the most perplexing main problems of modern physics, become rigorously, intimately mathematically related, by having the same qualitative {\it dynamical} roots. Ultimately our main point is meta-mathematical, as far as modern physics is concerned: due to the discrete group-theoretic conceptual simplicity of the theory, with its group-theoretic 'Planckian membrane/discreteness' starting point, {\it the fact that it is not just a mere mathematical model,} and all its properties above, any other {\it mathematically rigorous} approach has to built on AP Theory and be topologically absorbed and enveloped by it.