Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Towards an Action Principle Unifying the Standard Model and Gravity

Pedro D. Alvarez, Fernando Izaurieta, Cristian Quinzacara

TL;DR

Addresses unification of the Standard Model with gravity without extra dimensions or ad hoc symmetry breaking. It develops a Clifford-algebra-valued curvature approach with an induced dual operator and an osp(n,4) embedding, packaging all fields into a single gauge connection and yielding invariants that reproduce the canonical Yang–Mills, spin-$\tfrac{1}{2}$ fermion, and ghost-free quadratic gravity dynamics, with a dynamically induced Hodge dual. A special choice of parameters recovers the ghost-free Sezgin model for gravity with propagating torsion, while cancellations ensure canonical fermion kinetics; the tetrad acts as part of the dual operator rather than an independent gauge field. Interpreted as a low-energy effective theory, the construction offers a geometrically economical unification with potential extensions to superconformal algebras and cosmology.

Abstract

A single geometric invariant fixes the relative normalization and structure of gravity, Yang-Mills theory, and fermion kinetic terms -- including ghost freedom in the gravitational sector -- without tuning. Our results establish a minimal geometric route to unification that does not rely on extra dimensions or symmetry breaking by hand. Unlike previous gauge-gravity constructions, the relative normalizations and ghost freedom emerge from a single Clifford-algebraic invariant, without explicit symmetry breaking.

Towards an Action Principle Unifying the Standard Model and Gravity

TL;DR

Addresses unification of the Standard Model with gravity without extra dimensions or ad hoc symmetry breaking. It develops a Clifford-algebra-valued curvature approach with an induced dual operator and an osp(n,4) embedding, packaging all fields into a single gauge connection and yielding invariants that reproduce the canonical Yang–Mills, spin- fermion, and ghost-free quadratic gravity dynamics, with a dynamically induced Hodge dual. A special choice of parameters recovers the ghost-free Sezgin model for gravity with propagating torsion, while cancellations ensure canonical fermion kinetics; the tetrad acts as part of the dual operator rather than an independent gauge field. Interpreted as a low-energy effective theory, the construction offers a geometrically economical unification with potential extensions to superconformal algebras and cosmology.

Abstract

A single geometric invariant fixes the relative normalization and structure of gravity, Yang-Mills theory, and fermion kinetic terms -- including ghost freedom in the gravitational sector -- without tuning. Our results establish a minimal geometric route to unification that does not rely on extra dimensions or symmetry breaking by hand. Unlike previous gauge-gravity constructions, the relative normalizations and ghost freedom emerge from a single Clifford-algebraic invariant, without explicit symmetry breaking.
Paper Structure (14 sections, 47 equations, 2 tables)

This paper contains 14 sections, 47 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Construction of quadratic invariants
  3. Discussion and Outlook
  4. Clifford-algebra contractions and quadratic curvature invariants
  5. Contractions involving the Hodge dual
  6. Definition of the quadratic invariants
  7. Contractions using Clifford--algebra--valued frame
  8. Tangent-space Gamma matrices
  9. Quadratic terms of the fermionic curvature
  10. More contractions using Clifford--algebra--valued frame
  11. From the $A/S$ pair-exchange split to spin--parity modes
  12. Pair-exchange operator and the $A/S$ decomposition
  13. Contortion expansion and linearized interpretation
  14. Spin--parity content: why $\mathbf{2}^+$ is in $S$, and torsion modes arise from $A$