A Conditional Gap Criterion in Fried's Nonperturbative QCD Functional Formalism
Year: 2026
Type: preprint
Abstract: We formulate a conditional gap criterion within Fried’s nonperturbative QCD functionalformalism. On the natural self-dual Fried–Schur branch, the physical closed-current sectordecomposes under the diagonal color-spatial SO(3) as3 ⊗ 3 = 1 ⊕ 3 ⊕ 5.The antisymmetric triplet is identified with the branch-orientation orbit and is removed in thephysical quotient, leaving only the singlet and fiveplet current channels. The branch-dressedrenormalized two-point loop tensor Πai,bj (u), with u = q2/m2, determines two physical momentshifts,m1 = T ′2(0)3 , m5 = 3T ′1(0) − 2T ′2(0) + 3T ′3(0)30 ,whereT1 = Πai,ai, T2 = δaiδbj Πai,bj , T3 = δaj δbiΠai,bj .Let Z(0)1 , Z(0)5 > 0 denote the bare local physical current stiffnesses in the singlet and fivepletchannels. We show that ifm1 + ε1 < Z(0)1 , m5 + ε5 < Z(0)5 ,where ε1, ε5 bound negative compact residuals in the two physical channels, then the physicalquadratic closed-current kernel satisfiesK(j)phys(p) ≥ bFried(p2 + m2)with bFried > 0. Assuming further a physical transfer-matrix reconstruction and a regulator-uniform polymer estimate for the nonlinear branch-dressed vertices, the physical gap obeys∆ ≥ pbFried CFriedG ΛYM > 0.In the minimal self-dual normalization, Z(0)1 = Z(0)5 = 2. As an explicit model calculation, weevaluate the chain-loop approximation and findm1 = m5 = Cloop30m2M 2loop.Thus, in the minimal normalization, the chain-loop sector is stable providedCloopm2M 2loop< 60.The result is a conditional Fried–Schur positivity criterion for physical closed-current kernels,reducing the remaining gap problem in this framework to two branch-dressed current-channelmoment estimates, a transfer-matrix positivity/reconstruction hypothesis, and a uniform non-linear polymer bound.
Author: Tsang, Peter H.
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7163169423
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