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 $SU(N)$ theories with one hypermultiplet in the antisymmetric representation and to the case of 5d pure $USp(2N)$ 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.

51 pages, 23 figures. v2, minor clarifications in section 3

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Cited by in corpus (10)

• Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective
• Dualities and 5-brane webs for 5d rank 2 SCFTs
• 5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories
• 5d/6d DE instantons from trivalent gluing of web diagrams
• A slow review of the AGT correspondence
• More on topological vertex formalism for 5-brane webs with O5-plane
• Instanton counting and O-vertex
• Exploring the orthosymplectic zoo
• Refined topological vertex with ON-planes
• Instantons on Young diagrams with matters