Flop Invariance of Refined Topological Vertex and Link Homologies

Abstract

It has been proposed recently that the topological A-model string theory on local toric Calabi-Yau manifolds has a two parameter extension. Amplitudes of the two parameter topological strings can be computed using a diagrammatic method called the refined topological vertex. In this paper we study properties of the refined amplitudes under the flop transition of toric Calabi-Yau three-folds. We also discuss that the slicing invariance and the flop transition imply a simple formula for the homological sl(N) invariants of the Hopf link. The new expression for the invariants gives a simple refinement of the Hopf link invariant of Chern-Simons theory.

15 pages, 3 figures

References in corpus (5)

• The Refined Topological Vertex
• Les Houches lectures on matrix models and topological strings
• Curve counting and instanton counting
• Topological strings and their physical applications
• Conjectures on the cohomology of the Grassmannian

Cited by in corpus (6)

• Fiber-Base Duality and Global Symmetry Enhancement
• Kerov functions for composite representations and Macdonald ideal
• Surface defects on E-string from 5-brane webs
• Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
• Hopf superpolynomial from topological vertices
• Affine SU(N) algebra from wall-crossings