Holographic topological defects in a ring: role of diverse boundary conditions

TL;DR

This paper explores how different boundary conditions in holographic models influence the formation and properties of topological defects during phase transitions, revealing distinct behaviors in superfluid and superconductor states.

Contribution

It demonstrates how Dirichlet and Neumann boundary conditions lead to different topological defect configurations and correlation functions in holographic superfluid and superconductor models.

Findings

Holographic superfluid exhibits persistent superflow and cosine correlation functions.

Holographic superconductor lacks superflow and shows rapidly decaying correlations.

Boundary conditions critically affect topological defect formation and behavior.

Abstract

We investigate the formation of topological defects in the course of a dynamical phase transition with different boundary conditions in a ring from AdS/CFT correspondence. According to the Kibble-Zurek mechanism, quenching the system across the critical point to symmetry-breaking phase will result in topological defects -- winding numbers -- in a compact ring. By setting two different boundary conditions, i.e., Dirichlet and Neumann boundary conditions for the spatial component of the gauge fields in the AdS boundary, we achieve the holographic superfluid and holographic superconductor models, respectively. In the final equilibrium state, different configurations of the order parameter phases for these two models indicate a persistent superflow in the holographic superfluid, however, the holographic superconductor lacks this superflow due to the existence of local gauge fields. The two-point correlation functions of the order parameter also behave differently. In particular, for holographic superfluid the correlation function is a cosine function depending on the winding number. The correlation function for the holographic superconductor, however, decays rapidly at short distances and vanishes at long distance, due to the random localities of the gauge fields. These results are consistent with our theoretical analysis.