Kibble-Zurek mechanism and beyond in a holographic superfluid disk

Crossing a continuous phase transition in finite time induces spontaneous symmetry breaking and the formation of topological defects, such as domain walls and vortices. The AdS/CFT correspondence provides a framework for studying strongly coupled critical dynamics via a dual gravitational theory. We investigate the normal-to-superfluid phase-transition dynamics and the spontaneous vortex formation while crossing the critical temperature in a disk geometry by solving the Einstein-Abelian-Higgs model in an AdS₄ black hole. For slow quenches, the vortex density follows the Kibble-Zurek mechanism (KZM) scaling with the cooling rate, whereas for fast quenches it scales universally with the final temperature, beyond the KZM predictions. Although vortex number distributions appear normal, the study of cumulants reveals non-normal features consistent with Poisson binomial statistics, confirmed by their scaling with the quench time and depth. Our results support a universal defect distribution that encompasses KZM scaling, its breakdown, and universal quench-depth scaling at fast quenches.