Table 2: 𝑈 ( 1 ) 4 charges and 𝑍 𝑁 × 𝑍 𝑁 orbifold action 𝑁 -alities for the matter hypermultiplets.

𝑄 𝑄 Λ 1 Λ 2 Λ 3 Λ 4 Λ 1 Λ 2 Λ 3 Λ 4 𝐹 𝐹

𝑞 1 00−1/2+1/2−1/2+1/2+1/2−1/2+1/2−1/200
𝑞 2 00+1/2−1/2−1/2+1/2−1/2+1/2+1/2−1/200
𝑞 3 00+1/2+1/2−1/2−1/2+1/2+1/2−1/2−1/211
𝑞 4 +1/2+1/200000000−1/2−1/2

𝑟 1 00−10010−110−1−1
𝑟 2 000−101−1010−1−1