Dynamics of ($Z_N$) Domain Walls in SU(N) Gauge Theories

Sayanjit Banerjee; Sanatan Digal; Sumit Shaw

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arXiv · 2606.22532

Dynamics of ($Z_N$) Domain Walls in SU(N) Gauge Theories

Sayanjit Banerjee·Sanatan Digal·Sumit Shaw

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Abstract

We study collisions of domain walls in $SU(N)$ gauge theories using the Polyakov-loop effective potential models. We find that string junctions play a crucial role in the dynamics of $Z_N$ domain walls. In $SU(3)$ gauge theory, the merger of two non-planar $Z_3$ domain walls into a single wall proceeds via the creation of a vortex--antivortex pair in $2+1$ dimensions. In $SU(4)$ gauge theory, low-energy collisions of $Z_4$ walls result in the formation of a single domain wall without the creation of vortices. At higher collision energies, two $Z_4$ domain walls can either bounce back or scatter into another pair of domain walls through the formation of vortices. The creation of vortex--antivortex pairs generalises to the creation of string loops in $3+1$ dimensions for both gauge theories. These results demonstrate a direct dynamical role for topological strings in the evolution of center-domain-wall networks and reveal a new aspect of defect dynamics in non-Abelian gauge theories.

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Sayanjit Banerjee, Sanatan Digal, Sumit Shaw. 2026-06-21. Dynamics of ($Z_N$) Domain Walls in SU(N) Gauge Theories. https://arxiv.org/abs/2606.22532

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