What question did this study set out to answer?

This work aims to establish the Feynman rules for quantum field theory in a specific multi-dimensional geometric framework and derive its implications for particle physics.

March 18, 2026Open Access

Feynman Rules on the Spoke Geometry: Multi-Dimensional Propagators and the Derivation of Standard Model Couplings from D = 11

Key Points

This work aims to establish the Feynman rules for quantum field theory in a specific multi-dimensional geometric framework and derive its implications for particle physics.
Derived Feynman rules in the context of D = 11 dimensions with a hub-and-spoke geometry.
Defined propagators with multi-dimensional labels and characterized various types of vertices (electromagnetic, gravitational, strong).
Analyzed loop diagrams to derive coupling constants and other significant parameters.
Derived strong coupling constant α_s = αN²/3 from one-loop diagrams.
Identified a reverberation damping hierarchy of 1:42:98 from spoke-exchange topology.
Obtained a correction to the Higgs effective potential from KK mode exchange on hidden spokes.
Derived a dark matter fraction of (N−1)/N from graviton contributions.
Showed that strong CP leads to θ = 0 from spectral pairing of the boundary operator.

Abstract

We derive the Feynman rules for quantum field theory on the extended Randall-Sundrum hub-and-spoke geometry with D = 11 dimensions, N = 7 spokes, and warp depth kL = 37. Every propagator carries three labels: a 4D spacetime position xᵐ, a spoke index s ∈ 1,. . . , 7, and a bulk coordinate c ∈ 0, 1. Electromagnetic vertices are spoke-diagonal (conserving spoke number), gravitational vertices are spoke-universal (summing over all spokes), and strong vertices are spoke-pairing (connecting distinct spoke pairs). From these rules we derive: (i) the strong coupling constant αₛ = αN²/3 from the ratio of spoke-pairing to spoke-diagonal one-loop diagrams, (ii) the reverberation damping hierarchy 1: 42: 98 from spoke-exchange loop topology, (iii) the (1+1/kL) correction to the Higgs effective potential from KK mode exchange on each hidden spoke, (iv) the dark matter fraction (N−1) /N from the graviton spoke-sum, and (v) the strong CP result θ = 0 from Z₂ spectral pairing of the boundary Dirac operator. The formalism provides rigorous derivations of results previously obtained by dimensional analysis and geometric argument, and generates new predictions for KK mode signatures at colliders.

Feynman Rules on the Spoke Geometry: Multi-Dimensional Propagators and the Derivation of Standard Model Couplings from D = 11

Key Points

Abstract

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