Musings

Topological Vertex

There’s a very interesting paper by Li, Liu, Liu & Zhou (my, how that rolls off the tongue!), which provides a mathematical formulation of the topological vertex by Aganagic, Klemm, Marino & Vafa. The claim of the latter is that one can construct the higher genus topological A-model invariants for a noncompact toric Calabi-Yau by summing trivalent Feynman graphs, whose vertex is the aforementioned “topological vertex.”

LLL&Z put this proposal on a firm mathematical footing using relative Gromov-Witten theory (which, if I understand correctly, has not previously found a role on the physics side).

Bogdan Florea pointed out to me that the LL&Z did not prove that their formula is equivalent to AKM&V’s formula for the topological vertex, though they have checked, in examples, that the two formulæ agree.