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Superconformal partition functions and non-perturbative topological strings. (English) Zbl 1402.81248

Summary: We propose a non-perturbative definition for refined topological strings. This can be used to compute the partition function of superconformal theories in 5 dimensions on squashed \(S^5\) and the superconformal index of a large number of 6 dimensional (2,0) and (1,0) theories, including that of \(N\) coincident M5 branes. The result can be expressed as an integral over the product of three combinations of topological string amplitudes. SL(3,\({\mathbb{Z}}\)) modular transformations acting by inverting the coupling constants of the refined topological string play a key role.

MSC:

81T60 Supersymmetric field theories in quantum mechanics
83E30 String and superstring theories in gravitational theory
81T45 Topological field theories in quantum mechanics
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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