More on topological vertex formalism for 5-brane webs with O5-plane
Hirotaka Hayashi, Rui-Dong Zhu

TL;DR
This paper introduces an O-vertex function for topological vertex formalism involving O5-planes, enabling computation of Nekrasov partition functions for 5d theories on 5-brane webs with O5-planes, and verifies its effectiveness through known gauge theories.
Contribution
It proposes a new O-vertex formalism extension for 5-brane webs with O5-planes, allowing explicit calculation of Nekrasov partition functions for various 5d gauge theories.
Findings
Successfully computed partition functions for SO(N) and G_2 gauge theories.
Validated results against known literature.
Extended the formalism to include Chern-Simons level in SU(3) theories.
Abstract
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 arXiv:1709.01928. 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() gauge theories and the pure 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 . At the end we rewrite the O-vertex in a form of a vertex operator.
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