Mesons and Tetraquarks as Topological Strings: Geometric Unification in QCD Phase Transitions

We present a geometric model of mesons and tetraquarks as topological strings emerging from curvature dynamics in quantum chromodynamics. Mesons correspond to closed strings (S1) with quark-antiquark singularities, while tetraquarks form knotted vortex configurations stabilized by non-local torsion. Key results:

(1) Mass-radius relation m = σL + ℏcRp⟨K⟩,

(2) Exotic state classification via knot polynomials,
(3) Predictive decay patterns from critical curvature κcrit = 2πmπ c/ℏ.

Experimental verification through
quantum simulation shows 89% fidelity for π+ and 87% for Zc(3900).