A mathematical theory of the topological vertex

By Jun Li, Chiu-Chu Melissa Liu, Kefeng Liu, Jian Zhou. 2004

176 citations recorded by the source corpus.

We have developed a mathematical theory of the topological vertex--a theory that was original proposed by M. Aganagic, A. Klemm, M. Marino, and C. Vafa in hep-th/0305132 on effectively computing Gromov-Witten invariants of smooth toric Calabi-Yau threefolds derived from duality between open string theory of smooth Calabi-Yau threefolds and Chern-Simons theory on three manifolds.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ae17a2a8cfb9491a75857ceba325efaeb8908726

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. R. Pandharipande
2. A. Okounkov
3. Davesh Maulik
4. B. Eynard
5. Marcos Mariño
6. Alexei Oblomkov
7. N. Orantin
8. H. Kanno

In Geometry and Topology

1. Marcos Mariño
2. R. Pandharipande
3. A. Okounkov
4. B. Eynard
5. Davesh Maulik
6. N. Orantin
7. H. Kanno
8. Alexei Oblomkov

In Mathematical Physics

1. R. Pandharipande
2. A. Okounkov
3. B. Eynard
4. Marcos Mariño
5. Davesh Maulik
6. N. Orantin
7. H. Awata
8. H. Kanno

Citations in the corpus

• Computation of Open Gromov–Witten Invariants for Toric Calabi–Yau 3-Folds by Topological Recursion, a Proof of the BKMP Conjecture (2012, background): “11 03 v2 [ m at”
• Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds (2008, result): “19, 28]. The 2-leg case was proven in [20]. Finally, an evaluation of the Gromov-Witten theory of a local Calabi-Yau toric 3-fold X in a form closely resembling the topological vertex was obtained in [17]. 4.1.2 Stable pairs The virtual enumeration of stable pairs in the derived category of X was co”
• Instanton counting, Macdonald function and the moduli space of D-branes (2005, background): “Since the topological partition function gives the generating function of topological invariants, the equalities imply rather surprising mathematical conjectures on the relation of invariants that seem to have quite different origin at the first sight.”
• Chern-Simons theory and topological strings (2004, methodology): “Some steps in this direction have been already taken by Diaconescu and Florea (2003), and Li et al. (2004) have given a mathematical treatment of the topological vertex by using relative Gromov-Witten invariants.”