qcd_no_af_nf17
plain-language theorem explainer
The theorem establishes that the one-loop beta coefficient in three-color QCD with seventeen fermion flavors is negative, so the coupling is not asymptotically free. Researchers mapping the QCD conformal window cite this bound when locating the transition from confining to conformal behavior. The proof is a one-line wrapper that substitutes the specialized coefficient expression for seventeen flavors and reduces the arithmetic numerically.
Claim. For SU(3) Yang-Mills theory coupled to seventeen Dirac fermions the one-loop beta-function coefficient satisfies $b < 0$.
background
The QFT anomalies module derives quantum anomalies from eight-tick phase mismatches between discrete time structure and continuous symmetries. The beta coefficient governs the running of the gauge coupling; its sign determines whether the theory is asymptotically free. Upstream results include the spectral emergence structure that fixes the gauge content to SU(3) × SU(2) × U(1) together with three generations, and the ledger factorization that calibrates the underlying J-cost.
proof idea
The proof rewrites the beta coefficient using the seventeen-flavor specialization and then applies numerical normalization to obtain the strict inequality.
why it matters
This result is invoked by the theorem that places the critical flavor count strictly between sixteen and seventeen. It supports the Recognition Science derivation of the conformal anomaly from eight-tick phase quantization, consistent with the module target of obtaining anomalies from discrete time. The placement aligns with the eight-tick octave and the D = 3 spatial dimensions fixed earlier in the forcing chain.
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