More on topological vertex formalism for 5-brane webs with O5-plane

We propose a concrete form of a vertex function, which we call O-vertex, for the intersection between an O5-plane and a 5-brane in the topological vertex formalism, as an extension of the work of [1]. Using the O-vertex it is possible to compute the Nekrasov partition functions of 5d theories realized on any 5-brane web diagrams with O5-planes. We apply our proposal to 5-brane webs with an O5-plane and compute the partition functions of pure SO(N) gauge theories and the pure G(2) gauge theory. The obtained results agree with the results known in the literature. We also compute the partition function of the pure SU(3) gauge theory with the Chern-Simons level 9. At the end we rewrite the O-vertex in a form of a vertex operator.

Automated summary

A concrete form of a vertex function called O-vertex was proposed for the intersection between an O5-plane and a 5-brane in the topological vertex formalism. The Nekrasov partition functions of 5d theories on 5-brane web diagrams with O5-planes were computed using the O-vertex, with results agreeing with existing literature. Additionally, partition functions for pure SU(3) gauge theory with Chern-Simons level 9 were also calculated.