Topological strings and 5d T_N partition functions

Understand

We evaluate the Nekrasov partition function of 5d gauge theories engineered by webs of 5-branes, using the refined topological vertex on the dual Calabi-Yau threefolds.

• The theories include certain non-Lagrangian theories such as the T_N theory.
• The refined topological vertex computation generically contains contributions from decoupled M2-branes which are not charged under the 5d gauge symmetry engineered.
• We argue that, after eliminating them, the refined topological string partition function agrees with the 5d Nekrasov partition function.