String Solutions in Topological Phase Transitions: Geometric Approach to Confinement and Mass Spectrum

We present a geometric mechanism for string emergence from topological phase transitions inquantum chromodynamics. Unlike fundamental string theories, our model derives relativistic stringsdynamically through sphere-torus (S2 ⇌ T 2) transitions. Key results include: (1) Confinement as topological closure (π1(T 2)̸ = 0), (2) Tachyon-free mass spectrum(3) Minimal length Lmin = 2π√α′ ≈ 1.3 fm. Quantum simulations show 92% fidelity for J/ψ stringimplementation. The framework naturally incorporates gravity when ⟨K⟩ = 0.我们提出了一种源于量子色动力学（quantum chromodynamics, QCD）拓扑相变的弦涌现几何机制。与基本弦理论不同，本模型通过球面-环面（S² ⇌ T²）相变动态导出相对论性弦。核心研究结果如下： (1) 禁闭作为拓扑闭包（π₁(T²) ≠ 0）；(2) 无快子质量谱；(3) 最小长度$L_{ ext{min}} = 2pisqrt{alpha'} approx 1.3$ 飞米（fm）。 量子模拟结果显示，J/ψ弦实现的保真度达92%。当⟨K⟩ = 0时，该框架可自然纳入引力。