Standard Model Symmetries and K(E_10) (2503.13155v1)

Abstract: We clarify and extend our earlier work (K.A.Meissner and H.Nicolai, Phys. Rev. D91 (2015) 065029 and Phys. Rev. Lett. 121 (2018) 091601) where it was shown how to amend a scheme originally proposed by M. Gell-Mann to identify the three families of quarks and leptons of the Standard Model with the 48 spin 1/2 fermions of N=8 supergravity that remain after absorption of eight Goldstinos, a scheme that in its original form is dynamically realized at the SU(3)xU(1) stationary point of gauged N=8 supergravity. We explain how to deform and enlarge this symmetry at the kinematical level to the full Standard Model symmetry group SU(3)c x SU(2)_w x U(1)_Y, with the correct charge and chiral assignments for all fermions. The framework also leaves room for an extra U(1)(B-L) symmetry. This symmetry enhancement is achieved by embedding the Standard Model symmetries into (a quotient group of) K(E_10), the maximal compact subgroup' of the maximal rank hyperbolic Kac-Moody symmetry E_10, and an infinite prolongation of the SU(8) R-symmetry of N=8 supergravity. This scheme, which is also supposed to encompass quantum gravity, cannot be realized within the framework of space-time based (quantum) field theory, but requires space-time and related geometrical concepts to beemergent'. We critically review the main hypotheses underlying this construction.

Standard Model Symmetries and K(E10)

The paper "Standard Model Symmetries and K(E10)" by Krzysztof A. Meissner and Hermann Nicolai explores a novel approach to the unification of fundamental interactions, specifically addressing the symmetries of the Standard Model (SM). The authors propose a theoretical framework that aims to explain the SM's fermions and symmetries through the lens of N=8 supergravity and its connection to hyperbolic Kac-Moody algebra E10. This research builds on Gell-Mann's proposal to link the 48 fermions of the SM with N=8 supergravity's 48 spin-1/2 fermions after absorbing eight Goldstinos.

Core Hypotheses and Approach

The central premise of the paper is that the SM symmetries can be embedded into the structure provided by the infinite-dimensional symmetry group K(E10), which is a 'maximal compact subgroup' of E10. This embedding incorporates the SM gauge group SU(3)c×SU(2)w×U(1)y and facilitates the inclusion of an additional U(1)B-L symmetry. Unlike conventional theories relying on grand unification or superstring compactifications, this approach does not necessitate the introduction of numerous new degrees of freedom — a significant deviation from traditional paradigms.

Symmetry Enhancement and Implications

The authors argue how a symmetry enhancement at the kinematical level to encompass full SM symmetries is achieved. They detail the mapping of SM fermions to the N=8 spin-1/2 fermions and elaborate on the charge assignments necessitated by this scheme. An additional aspect tackled is the embedding of these symmetries within K(E10) via quotient groups associated with unfaithful representations of K(E10).

In terms of implications, the paper makes three bold predictions compensating for decades of experimental no-shows regarding new fundamental particles:

1. Strict adherence to three families of SM fermions without new fundamental spin-1/2 fermions, e.g., gauginos or Higgsinos beyond said families.
2. The introduction of supermassive gravitinos, which are SM charges carrying and detectable in upcoming underground experiments.
3. An incompatibility with any form of space-time supersymmetry, suggesting either a novel supersymmetry breaking mechanism or its complete absence.

Challenge to Conventional Paradigms

This manuscript challenges the existing methodologies to derive SM structure from high-energy theories, notably addressing the lack of new particle evidence despite rigorous LHC exploration. Instead, it suggests that the conventional field-theoretical concepts and spatio-temporal dependencies are emergent properties, stemming from this algebraic framework driven by E10 symmetries.

Speculation and Future Directions

As revealing as this alternate approach is, the paper acknowledges undoubted challenges and unexplained dynamics, particularly regarding how chiral symmetries might dynamically arise to keep SM fermions massless while the Planck scale remains as the gravitational fermions’ natural mass scale. Further advancement towards complete spatial dependence inclusion and capturing larger coherent representations of K(E10) is emphasized.

The proposition to validate the existence of supermassive gravitinos adds an intriguing experimental speculation, offering a prospect for dark matter or cosmic ray origins examination. Additionally, expanding on mathematical and theoretical fronts related to hyperbolic Kac-Moody algebras would be essential for deeper insight and specification of spatial dependencies.

Overall, this paper provides a complex yet potentially critical perspective aiming for greater unification of forces, consistent SM charge assignments, and predictions that are ripe for empirical testing in the near future.