A Zero-Parameter Formula for the String Tension of SU(Nc) Yang–Mills Theory

We observe that the string tension of pure SU(Nc) Yang–Mills theory in the Sommer r₀ scheme is well described by the zero-parameter formula σΛ2=eπ(2π)d+1d−1−1Nc2σ/Λ^2 = {eπ}{(2π)d+1/d-1 - 1/N_c^2}Λ2σ=(2π)d−1d+1−Nc21eπ where d is the spacetime dimension. For d = 4 the exponent equals 5/3 − 1/Nc². Tested against Lucini–Teper–Wenger lattice data for Nc = 2–8, the formula achieves χ²/dof = 0.56 with zero free parameters, outperforming 99.99% of random four-parameter alternatives (3.8σ significance). Cross-checks with the Regge slope, the deconfinement ratio Tc/√σ, glueball mass scaling, and topological susceptibility are all consistent. We identify the physical origin of each factor: e^π arises as the BPS monopole action at the self-dual point on S³ × S¹; the exponent 5/3 decomposes into a spectral determinant computed via the Epstein zeta function (α_det = 1.344, exact), the Polchinski–Strominger worldsheet integral (α_PS = 0.096, exact), and an IR contribution consistent with the leading IR renormalon (α_IR ≈ 0.23). Several independent arguments — the trace anomaly combined with the Lüscher term, worldsheet CFT, and holographic models — all point to the same value 5/3 = 4/3 + 1/3. A falsifiable prediction is given for d = 3.