Standard model fermions and K(E10)

TL;DR

This paper explores how the K(E10) symmetry, a candidate for M-theory's underlying symmetry, can incorporate Standard Model fermions within a supergravity framework, suggesting new paths toward unifying quantum gravity and particle physics.

Contribution

It demonstrates that the necessary deformation for charge assignment alignment belongs to K(E10), linking Standard Model fermions to hyperbolic Kac-Moody symmetries in M-theory.

Findings

Deformation resides in K(E10), not SU(8)

K(E10) symmetry can embed Standard Model fermions

Hyperbolic symmetries are crucial for unification

Abstract

In recent work arXiv:1412.1715 it was shown how to modify Gell-Mann's proposal for identifying the 48 quarks and leptons of the Standard Model with the 48 spin-1/2 fermions of maximal SO(8) gauged supergravity that remain after the removal of eight Goldstinos, by deforming the residual U(1) symmetry at the SU(3)xU(1) stationary point of N=8 supergravity to also achieve agreement of the electric charge assignments. In this Letter we show that the required deformation, while not in SU(8), does belong to K(E10), the `maximal compact' subgroup of E10 which is a possible candidate symmetry underlying M theory. The incorporation of infinite-dimensional Kac-Moody symmetries of hyperbolic type, apparently unavoidable for the present scheme to work, opens up completely new perspectives on embedding Standard Model physics into a Planck scale theory of quantum gravity.