In a physics paper entitled "Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces" by Intriligator, Morrison and Seiberg, the authors write an equation
$$2\pi \frac{c_{ijk}}{6}\int_{Y}\left(\frac{F^i}{2\pi}\right)\wedge\left(\frac{F^j}{2\pi}\right)\wedge\left(\frac{F^k}{2\pi}\right) \equiv 2\pi i \frac{c_{ijk}}{6} c_1(L^i)c_1(L^j)c_1(L^k)$$
(This is equation 2.7 on page 5 of the paper.)
This is the extension of the Chern Simons term on a 5-manifold $W$ which is the boundary of a 6-manifold $Y$ (so $W = \partial Y$).
How does one arrive at this equality? The left-hand side is the integral of a 6-form, and the right-hand side has a product of three first Chern classes. What are the underlying mathematical theorems being used here?
When can the triple intersection number be written as a product of Chern classes over (complex) line bundles in this form?
EDIT: Following some statements on page 8 of a related paper by Witten entitled "Phase Transitions in M- and F- Theory", I can say that $L^i$'s are complex line bundles over the oriented six-manifold $Y$. But the equality above is still unclear to me.
I don't think there's anything underhanded going on here. The Chern class of a line bundle $L$ is represented by the form $\dfrac{\sqrt{-1}}{2\pi} F^L$. Wedge product of closed forms corresponds to cup product of the corresponding cohomology classes. So you need to interpret the right-hand side as a product in cohomology of $Y$ (rel boundary). Algebro-geometrically, you can think of the Chern classes as divisors (complex codimension-1 submanifolds) and then intersect the three. I don't know much about this theory, but I assume that these are going to be compact and away from $\partial Y$.
You should let me know if I've missed a subtlety.