Evolution of Vortex Strings after a Thermal Quench in a Holographic Superfluid

The formation of topological defects during continuous phase transitions exhibits nonequilibrium universality. While the Kibble-Zurek mechanism (KZM) predicts universal scaling of point-like defect numbers under slow driving, the statistical properties of extended defects remain largely unexplored across both slow and fast protocols. We investigate vortex string formation in a three-dimensional holographic superfluid. For slow quenches, the vortex string number follows KZM scaling, while for rapid quenches, it exhibits complementary universal scaling governed by the final temperature. Beyond the vortex string number, the loop-length distribution reveals a richer structure: individual loops follow the first-return statistics of three-dimensional random walks, $P(\ell) \sim \ell^{-5/2}$. While the total vortex length distribution remains Gaussian, its cumulants obey universal scaling laws with varying power-law exponents, and thus differ markedly from those observed in point-defect systems, indicating distinct statistical features of extended topological defects.