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Flop Invariance of Refined Topological Vertex and Link Homologies
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In this article, the authors studied the properties of the refined amplitudes under the flop transition of toric Calabi-Yau three-folds and gave a simple formula for the homological sl(N) invariants of the Hopf link.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.read more
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Refined bps state counting from nekrasov's formula and macdonald functions
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Refined BPS state counting from Nekrasov's formula and Macdonald functions
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TL;DR: In this paper, a refined version of the topological vertex (hep-th/0502061) is a building block of the Nekrasov's partition function with two equivariant parameters.
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TL;DR: In this paper, the characters of GLn over a finite field and the Hecke ring of GLs over finite fields have been investigated and shown to be symmetric functions with two parameters.
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The Topological Vertex
TL;DR: In this paper, a cubic field theory was constructed for all genus amplitudes of the topological A-model for all non-compact toric Calabi-Yau threefold.
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Mikhail Khovanov,Lev Rozansky +1 more
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TL;DR: In this article, a new duality involving topological strings in the limit of the large string coupling constant is proposed, described in terms of a classical statistical mechanical model of crystal melting, where the temperature is the inverse of the string coupling constants.
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The Refined Topological Vertex
TL;DR: In this paper, a refined topological vertex which depends in addition on a parameter is defined, which physically corresponds to extending the self-dual graviphoton field strength to a more general configuration.