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

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arxiv 1707.05347 v1 pith:VV4IHCIH submitted 2017-07-17 hep-th

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

classification hep-th
keywords dualitygravitym-theoryquantumtopologicalhilbertloopm-branes
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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