Table 1: 𝑈 ( 1 ) 4 charges and 𝑍 𝑁 × 𝑍 𝑁 orbifold action 𝑁 -alities for the gauge multiplet, after modification of (3.24) to accomodate hypermultiplets. The second line connects to the CKKU notation for the fields 𝑧 3 , 𝜉 2 , 𝜉 1 , and so forth.

𝑧 1 𝑧 2 𝑖 𝜙 Ψ 1 Ψ 2 Ψ 3 Ψ 4 Ψ 1 Ψ 2 Ψ 3 Ψ 4 𝐺 𝐷
𝑧 3 𝜉 2 𝜉 1 𝜉 3 𝜆 𝜓 1 𝜓 2 𝜒 𝜓 3

𝑞 1 100−1/2+1/2−1/2+1/2+1/2−1/2+1/2−1/200
𝑞 2 010+1/2−1/2−1/2+1/2−1/2+1/2+1/2−1/200
𝑞 3 001−1/2−1/2+1/2+1/2−1/2−1/2+1/2+1/200
𝑞 4 000−1/2−1/2−1/2−1/2+1/2+1/2+1/2+1/2−10

𝑟 1 10−101−10100−100
𝑟 2 01−110−10010−100