Chern-Simons: Fano and Calabi-Yau

Table 1

Brane probes and associated world-volume physics in various backgrounds.

Brane probe	Theory	Background	World-volume theory	Vacuum moduli space
D5	Type IIB	ℝ^1,5×𝐶𝑌2	(5+1)-d 𝒩=1 gauge theory	CY2
D3	Type IIB	ℝ^1,3×𝐶𝑌3	(3+1)-d 𝒩=1 gauge theory	CY3
M2	M-theory	ℝ^1,2×𝐶𝑌4	(2+1)-d 𝒩=2 Chern-Simons	CY4