Seminar detail: Non-Abelian A_4 vortices in SO(3) gauge theory and non-invertible symmetries

Date&Time	Tue Nov 17 2026 (17:00 - 18:00)
Speaker	Ryo Yokokura
Affiliation	Keio University
Title	Non-Abelian A_4 vortices in SO(3) gauge theory and non-invertible symmetries
Abstract	We construct finite-tension non-Abelian vortex solutions in a renormalizable (3+1)-dimensional SO(3) gauge theory Higgsed to the tetrahedral group A_4 by a Higgs field in the spin-3 representation. Since the vacuum manifold is SO(3)/A_4, the vortices are characterized by the non-Abelian fundamental group \pi_1(SO(3)/A_4)\simeq \tilde{A}_4, the binary tetrahedral group. We obtain explicit axisymmetric vortex solutions carrying holonomies corresponding to the order-two and order-three conjugacy classes of A_4, determine their tensions numerically, and show that they exhibit type-I, type-II, and Bogomol'nyi--Prasad--Sommerfield-like behavior depending on the Higgs and gauge boson mass ratios. The vortices are classified by conjugacy classes of \tilde{A}_4, while their infrared descriptions are labeled by conjugacy classes of A_4. We further demonstrate that the smooth finite-tension vortices reduce in the infrared to Gukov--Witten surface operators of the A_4 discrete gauge theory, thereby establishing a finite-energy ultraviolet completion of non-invertible defects in a renormalizable gauge-Higgs theory.
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