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Partition functions of web diagrams with an \(O7^{-}\)-plane. (English) Zbl 1377.83121

Summary: 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(2\(N\)) 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.

MSC:

83E30 String and superstring theories in gravitational theory
81T60 Supersymmetric field theories in quantum mechanics
81T45 Topological field theories in quantum mechanics
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