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

• Published in: The journal of high energy physics Vol. 2021; no. 4; pp. 1 - 53
• Main Authors: Hayashi, Hirotaka, Zhu, Rui-Dong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2021; Springer Nature B.V; SpringerOpen
• Subjects: Branes; Classical and Quantum Gravitation; Elementary Particles; Formalism; Gauge theory; High energy physics; Operators (mathematics); p-branes; Partitions (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Duality; String Theory; Supersymmetry and Duality; Topological Strings; Topology; Webs; Topological Strings; p-branes; Supersymmetry and Duality; String Duality
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP04(2021)292

A bstract 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.