A Proof of the Full Marino-Vafa Conjecture
Jian Zhou
TL;DR
This paper proves the full Marino-Vafa Conjecture, establishing a precise link between open string invariants of the resolved conifold and Chern-Simons knot invariants, advancing understanding in mathematical physics and string theory.
Contribution
It provides the first complete proof of the Marino-Vafa Conjecture, connecting string invariants with quantum knot invariants.
Findings
Confirmed the conjecture's predictions for open string invariants.
Established the equivalence between open string invariants and Chern-Simons quantum dimensions.
Enhanced mathematical understanding of the relationship between string theory and knot invariants.
Abstract
We present a proof of the full Mari\~no-Vafa Conjecture that identifies certain open string invariants of the resolved conifold with the Chern-Simons knot invariant of the unknot, i.e. the quantum dimensions.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology