Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds

By Davesh Maulik, Alexei Oblomkov, A. Okounkov, R. Pandharipande. 2008

174 citations recorded by the source corpus.

We prove the equivariant Gromov-Witten theory of a nonsingular toric 3-fold X with primary insertions is equivalent to the equivariant Donaldson-Thomas theory of X. As a corollary, the topological vertex calculations by Agangic, Klemm, Mariño, and Vafa of the Gromov-Witten theory of local Calabi-Yau toric 3-folds are proven to be correct in the full 3-leg setting.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e62d69a0d403e7193e04ce914e539e130eb6c078

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The Gopakumar-Vafa formula for symplectic manifolds (2013, methodology): “GW/DT correspondence by calculating both sides explicitly in a computational tour de force [MOOP11].”
Curves on K3 surfaces and modular forms (2010, unknown): “We prove a Gromov-Witten/Pairs correspondence for toric 3-folds following [ 36 ].”
Lectures on K-theoretic computations in enumerative geometry (2015, background): “The theory is built so that this operator is the fundamental solution of the quantum differential equation and this is how [57] works.”
Computation of Open Gromov–Witten Invariants for Toric Calabi–Yau 3-Folds by Topological Recursion, a Proof of the BKMP Conjecture (2012, unknown): “11 03 v2 [ m at”
Gromov-Witten/pairs correspondence for the quintic 3-fold (2012, methodology): “To prove the correspondence for the capped rubber contributions over Y∞, we follow the technique developed in [21] where the capped rubber contributions for An ×P(1) /An × {∞} over ∞ were studied.”