A new duality between Topological M-theory and Loop Quantum Gravity

TL;DR

This paper proposes a duality between topological M-theory and loop quantum gravity, linking gravitational holonomies to M-branes and interpreting the Hamiltonian constraint as M-brane dynamics.

Contribution

It introduces the ${f H}$-duality conjecture that unifies topological M-theory with LQG through a novel Hilbert space correspondence.

Findings

Holonomies in LQG correspond to space-like M-branes.

Spinfoam models capture non-perturbative M-brane dynamics.

Hamiltonian constraint relates to M-brane nucleation and decay.

Abstract

Inspired by the long wave-length limit of topological M-theory, which re-constructs the theory of $3+1$D gravity in the self-dual variables' formulation, we conjecture the existence of a duality between Hilbert spaces, the ${\bf H}$-duality, to unify topological M-theory and loop quantum gravity (LQG). By ${\bf H}$-duality non-trivial gravitational holonomies of the kinematical Hilbert space of LQG correspond to space-like M-branes. The spinfoam approach captures the non-perturbative dynamics of space-like M-branes, and can be claimed to be dual to the S-branes foam. The Hamiltonian constraint dealt with in LQG is reinterpreted as a quantum superposition of SM-brane nucleations and decays.