<p>The long-range order and intrinsic entanglement of polymer play a crucial role in crystallization and the corresponding melting relaxation which, however, are rarely treated as a form of symmetry. In this work, a field model is developed based on a self-avoiding random string with open ends, where time dimension for string vibrations is added and the dynamics of chain vibrations is captured by <i>ϕ</i>⁴ a theory with O(<i>N</i>) symmetry. The long-range order triggered by crystallization is referred to the scalar’s breaking in grand canonical ensemble, while entanglement is considered as a geometric dynamic effect in absence of closed loops, rather than chain topology. For the entanglement, there are interactions among the replica scalar’s components <i>via</i> the gauged O(<i>N</i>) symmetry. The infrared stability at <i>d</i> = 3 + 1 requires <i>N</i> = 2, thus the gauge-scalar theory is reduced to Coleman-Weinberg model in the rest frame. The finite-temperature effect causes the second-order phase transition related to scalar’s breaking to become first-order with a metastable region, depending on the gauge coupling <i>g</i>. These modeling results are helpful in understanding the crystallization and melting behavior of polymer, including the difference of the extrapolated temperatures in Gibbs-Thomson equation, and the re-entanglement and the vanishing of long-range order in melt relaxation.</p>