Topological vertex for Higgsed 5d TN theories

Abstract

We analyse the computation of the partition function of 5d TN theories in Higgs branches using the topological vertex. The theories are realised by a web of (p, q) 5- branes whose dual description may be given by an M-theory compactification on a certain local non-toric Calabi-Yau threefold. We explicitly show how it is possible to directly apply the topological vertex to the non-toric geometry. Using this novel technique, which considerably simplifies the computation by the existing method, we are able to compute the partition function of the higher rank E6, E7 and E8 theories. Moreover we show how in some specific cases similar results can be extended to the computation of the partition function of 5d TN theories in the Higgs branch using the refined topological vertex. These cases require a modification of the refined topological vertex