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arxiv: hep-th/0701156 · v2 · submitted 2007-01-17 · ✦ hep-th

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The Refined Topological Vertex

Amer Iqbal , Can Kozcaz , Cumrun Vafa
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classification ✦ hep-th
keywords refinedvertextopologicaladditioncomputeconfigurationcorrespondsdefine
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We define a refined topological vertex which depends in addition on a parameter, which physically corresponds to extending the self-dual graviphoton field strength to a more general configuration. Using this refined topological vertex we compute, using geometric engineering, a two-parameter (equivariant) instanton expansion of gauge theories which reproduce the results of Nekrasov. The refined vertex is also expected to be related to Khovanov knot invariants.

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    A new shell formula unifies and delivers explicit closed-form expressions plus recursions for instanton partition functions in 5d SYM and multiple gauge origami configurations using arbitrary-dimensional Young diagrams.