Partition functions of web diagrams with an O7$^-$-plane
Abstract
We consider the computation of the topological string partition function for 5-brane web diagrams with an O7-plane. Since upon quantum resolution of the orientifold plane these diagrams become non-toric web diagrams without the orientifold we are able to apply the topological vertex to obtain the Nekrasov partition function of the corresponding 5d theory. We apply this procedure to the case of 5d theories with one hypermultiplet in the antisymmetric representation and to the case of 5d pure theories. For these cases we discuss the dictionary between parameters and moduli of the 5d gauge theory and lengths of 5-branes in the web diagram and moreover we perform comparison of the results obtained via application of the topological vertex and the one obtained via localisation techniques, finding in all instances we consider perfect agreement.
Keywords
Cite
@article{arxiv.1609.07381,
title = {Partition functions of web diagrams with an O7$^-$-plane},
author = {Hirotaka Hayashi and Gianluca Zoccarato},
journal= {arXiv preprint arXiv:1609.07381},
year = {2017}
}
Comments
51 pages, 23 figures. v2, minor clarifications in section 3