Conditional One-Loop Curvature Matching in the Axis Model
Andrew Morton · Public preprint · Conditional one-loop calculation
Calculates the one-loop curvature coefficient of a declared field theory and identifies the matching data needed for a physical gravitational interpretation.
Abstract
We calculate the local one-loop curvature coefficient of a declared minimal effective field theory and identify the additional data needed to interpret it as physical gravitational matching in the Axis Model. The conditional roster contains two real components of a neutral complex scalar, one matched photon, and a screened Abelian vector with an independent Stueckelberg compensator and Faddeev–Popov pair. In minimal Feynman gauge its leading curvature sum is S_min = −5/6 − ξ₁ − ξ₂, reducing to −5/6 − 2ξ for equal scalar curvature couplings. A normalized Hodge-mode calculation establishes the gauge-parameter cancellation of the Gaussian quotient, including its Proca measure factor; a common proper-time cutoff on the raw nonminimal operators instead gives gauge-dependent quadratic coefficients. We separate ultraviolet locality, mass thresholds, infrared contributions and finite matching. One reference condition determines a family of curvature coefficients, A = A_* + [fC − f_*C_*] + ΔA_loc, with G_EH/G_* = A_*/A. The familiar rational function is a restricted corollary. For an originating physical action we formulate a test of whether its computed coefficient difference factorizes as K(1 − f), retaining a different function when that test fails. Variable-coefficient field equations and conditional weak-field and lensing consequences complete the interface.
Scope
The one-loop result applies to a specified field roster and normalized Gaussian calculation. A physical action, its full fluctuation and constraint operator, a finite reference normalization and a map to measured gravitational forces remain separate inputs.
Paper and supporting files
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