String Field Theory from Quantum Gravity

TL;DR

This paper proposes a string field theory model based on quantum gravity and A(4) symmetries, linking neutrino oscillations to particle representations and a discretized quantum spacetime.

Contribution

It extends the EPRL quantum gravity model by coupling it with A(4) representations, connecting neutrino oscillations to a novel quantum field theory framework.

Findings

Reproduces standard model bosons and fermions via vacuum-changing operators.

Links A(4) representation labels to observable neutrino oscillations.

Proposes a discretized string field theory on quantum spacetime.

Abstract

Recent work on neutrino oscillations suggests that the three generations of fermions in the standard model are related by representations of the finite group A(4), the group of symmetries of the tetrahedron. Motivated by this, we explore models which extend the EPRL model for quantum gravity by coupling it to a bosonic quantum field of representations of A(4). This coupling is possible because the representation category of A(4) is a module category over the representation categories used to construct the EPRL model. The vertex operators which interchange vacua in the resulting quantum field theory reproduce the bosons and fermions of the standard model, up to issues of symmetry breaking which we do not resolve. We are led to the hypothesis that physical particles in nature represent vacuum changing operators on a sea of invisible excitations which are only observable in the A(4) representation labels which govern the horizontal symmetry revealed in neutrino oscillations. The quantum field theory of the A(4) representations is just the dual model on the extended lattice of the Lie group $E_6$, as explained by the quantum Mckay correspondence of Frenkel Jing and Wang. The coupled model can be thought of as string field theory, but propagating on a discretized quantum spacetime rather than a classical manifold.