A First-Principles Determination of the $SU(3)$ Gauge Coupling from an 11D--4D Effective Action
Year: 2026
Type: preprint
Abstract: We derive a current-normalized reference \(SU(3)\) gauge coefficient and construct its primitive geometric flux representative within an explicitly specified branch of an eleven-dimensional effective action. The parent information-projection theory supplies the higher-dimensional architecture and admissible variational setting. The strong-sector derivations are developed in the language of effective actions, Kaluza–Klein geometry, conserved color currents, associated bundles and gauge holonomy. The first principal result is the local action–current normalization. All action sectors are combined before the shared auxiliary fields are eliminated, and the transverse kinetic matrix is compared with the physical current through \[K_J=V_{Ja}^{-\dagger}K_{\mathrm{raw}}^{\mathrm{red}}V_{Ja}^{-1}.\] A maximally mixed three-level reference state and the stated current scores give the relative-entropy Hessian \[D^2\Gamma_{\mathrm{src}}(0)=(\ln 3)I_8.\] Its plaquette realization produces the local Yang–Mills operator. The same internal profile enters the action, an independent Kaluza–Klein curvature evaluation and the current norm, so the common factor \(7/8\) cancels. With the specified source-action law and no additional unmatched local term, \[K_A^{\mathrm{CN}}=I_8,\qquadg_3^{\mathrm{CN}}=1,\qquad\alpha_s^{\mathrm{CN}}=\frac{1}{4\pi}.\] The second principal result is a geometric and topological reconstruction through a distinct calculation. A correlated reference–color state with unchanged color marginal supplies a primitive associated line over \(SU(3)/U(1)_{(1,1)}\). We calculate its unit first-Chern pairing, construct a round color frame, and derive a spatial connection by minimizing the source hopping energy over all \(SU(3)\) links. For an oriented spherical triangle, its full Wilson matrix is \[W_{\triangle}=g_x\mathrm{e}^{\mathrm{i}Y\Omega_{\triangle}/2}g_x^{\dagger},\qquadY=\operatorname{diag}(1,1,-2),\] and its projected continuum curvature obeys \[-s_g^{\dagger}\widehat{\mathcal{F}}_{\star}s_g=f_B=\frac{\mathrm{d}\Omega}{2}.\] The primitive period, physical transport and generator norm thereby provide complementary checks of the action–current normalization. These routes share the declared source framework: topology fixes the flux unit and isotropy its distribution, while the action and physical current fix the strength. Joint stationary and finite-support realizations are distinguished from stability and free-core selection. A separate six-mass BFM-MOM prescription gives \[\mu_{\mathrm{CN}}=0.4167999616251471\,\mathrm{GeV}\] within the stated logarithmic functional class and a one-loop threshold interpolation from coefficient \(11\) to \(7\). The geometric reconstruction is not a second loop term. Matching an additional microscopic parent contribution, finite conversion to \(\overline{\mathrm{MS}}\), confinement and a Yang–Mills mass gap remain distinct questions.
Author: Lee, Dohyeong
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212589319
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