The Search for the Origins of M Theory : Loop Quantum Mechanics, Loops/Strings and Bulk/Boundary Dualities

TL;DR

This paper develops a covariant loop wave functional framework in a generalized 11D C-space to explore spacetime topology change, holography, and the origins of M theory, linking loop quantum mechanics and string theory through dualities.

Contribution

It introduces a covariant loop wave equation in a generalized 11D C-space and connects loop quantum mechanics with string theory via a bulk/boundary duality.

Findings

Spacetime topology change emerges from covariance in C-space.

A vacuum wavefunctional for SU(∞) Yang-Mills is constructed.

The approach suggests a new principle underlying M theory.

Abstract

The construction of a $covariant$ Loop Wave functional equation in a 4D spacetime is attained by introducing a generalized $eleven$ dimensional categorical {\bf C}-space comprised of $8\times 8$ antisymmetric matrices. The latter matrices encode the generalized coordinates of the histories of points, loops and surfaces $combined$. Spacetime Topology change and the Holographic principle are natural consequences of imposing the principle of $covariance$ in {\bf C}-space. The Planck length is introduced as a necessary rescaling parameter to establish the correspondence limit with the physics of point-histories in ordinary Minkowski space, in the limit $l_P\to 0$. Spacetime quantization should appear in discrete units of Planck length, area, volume ,....All this seems to suggest that the generalized principle of covariance, representing invariance of proper $area$ intervals in {\bf C}-space, under matrix-coordinate transformations, could be relevant in discovering the underlying principle behind the origins of $M$ theory. We construct an ansatz for the $SU(\infty)$ Yang-Mills vacuum wavefunctional as a solution of the Schroedinger Loop Wave equation associated with the Loop Quantum Mechanical formulation of the Eguchi-Schild String . The Strings/Loops ($SU(\infty)$ gauge field) correspondence implements one form of the Bulk/Boundary duality conjecture in this case.