Seminar detail: A New Class of Rank-Reducing Boundary Conditions on 2D Orbifolds and SU(9) GUT

Date&Time	Mon May 11 2026 (13:00 - 14:00)
Speaker	Toshifumi Yamashita
Affiliation	Aichi Medical University
Title	A New Class of Rank-Reducing Boundary Conditions on 2D Orbifolds and SU(9) GUT
Abstract	In this seminar, I will discuss a new class of rank-reducing boundary conditions in six-dimensional gauge theories compactified on the orbifolds $T^2/\mathbb{Z}_N$ ($N=2,3,4,6$) and their applications to electroweak symmetry breaking and grand unification. I will first present a systematic analysis of equivalence classes of orbifold boundary conditions in $SU(n)$ gauge theories, showing that while every class on $T^2/\mathbb{Z}_2$ and $T^2/\mathbb{Z}_3$ admits a diagonal representative, $T^2/\mathbb{Z}_4$ and $T^2/\mathbb{Z}_6$ allow genuinely non-diagonal block structures with discrete parameters. These new boundary conditions imply that rank-reducing symmetry breaking can be induced by discrete Wilson line phases. I will then explain how these boundary conditions, together with continuous Wilson line phases, can be used to construct gauge-Higgs unification models on $T^2/\mathbb{Z}_4$. In particular, I will discuss a minimal $SU(6)$ model that realizes electroweak symmetry breaking, in which two Higgs doublets arise from the extra-dimensional gauge field and quarks in each generation are unified into a single bulk multiplet without exotic zero modes. Finally, I will discuss an $SU(9)$ grand unified model obtained by unifying this $SU(6)$ electroweak model with the color group $SU(3)$. I will show that the model can accommodate the Standard Model matter content without exotic zero modes, that the gauge couplings approach one another around $10^6\,\mathrm{GeV}$, and that proton decay can be sufficiently suppressed.
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