Chern-Simons: Fano and Calabi-Yau

Table 3

The two phases of the (3+1)-dimensional gauge theory for the cone over the zeroth Hirzebruch surface 𝐹₀ beget 4 new QCS theories in (2+1) dimensions, the moduli spaces for which are cones over 4 different Fano threefolds.

𝐹0	CSLevels𝑘	𝑄𝑡	𝐺𝑡	∼𝐶𝑜𝑛𝑒(𝑋)
𝐼	(1,1,−1,−1)	11−11−1−100111−100−1−10000−1−111−1−1110000	000000−110000−1100−1100000011111111	𝒞3
𝐼	(−2,0,1,1)	0002−1−10000−1000100000−1−111−1−1110000	0−1−1000−110000−1100−1100000011111111	𝒞4
𝐼	(−2,1,0,1)	001−100−1100−1000010000−1−111−1−1110000	−100−110100000−1100−1100000011111111	𝒞5
𝐼𝐼	(−2,0,1,1)	0−200112−201−1000001−1000011−10−10011000−1−1110000−1−10	0−11000−10100−11000000000−11000111111111	𝒞4
𝐼𝐼	(−2,1,0,1)	01−100000000010000−101000−1−10100001−1−1101−1−1100000	−1001101010000−10010100−10−10−1−1111111111	𝒞1