On diagonal representatives in boundary condition matrices on orbifolds

Abstract

We study diagonal representatives of boundary condition matrices on the orbifolds $S^1/Z_2$ and $T^2/Z_m$ ($m=2,3,4,6$). We give an alternative proof of the existence of diagonal representatives in each equivalent class of boundary condition matrices on $S^1/Z_2$, using a matrix exponential representation, and show that they do not necessarily exist on $T^2/Z_2$, $T^2/Z_3$, and $T^2/Z_4$. Each equivalence class on $T^2/Z_6$ has a diagonal representative, because its boundary conditions are determined by a single unitary matrix.

arXiv comment15 pages, 3 figures

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Cited by in corpus (3)

• On representation matrices of boundary conditions in $SU(n)$ gauge theories compactified on two-dimensional orbifolds
• New classification method for Equivalence Classes on $S^1/Z_2$ and $T^2/Z_3$ Orbifolds
• Trace conservation laws in $T^2/Z_m$ orbifold gauge theories