Abstract
We study the stringy instanton partition function of four dimensional \( \mathcal{N}=2 \) U(N) supersymmetric gauge theory which was obtained by Bonelli et al. in 2013. In type IIB string theory on \( {\mathrm{\mathbb{C}}}^2\times {T}^{*}{\mathrm{\mathbb{P}}}^1\times \mathrm{\mathbb{C}} \), the stringy U(N) instantons of charge k are described by k D1-branes wrapping around the \( {\mathrm{\mathbb{P}}}^1 \) bound to N D5-branes on \( {\mathrm{\mathbb{C}}}^2\times {\mathrm{\mathbb{P}}}^1 \). The KK corrections induced by compactification of the \( {\mathrm{\mathbb{P}}}^1 \) give the stringy corrections. We find a relation between the stringy instanton partition function whose quantum stringy corrections have been removed and the K-theoretic instanton partition function, or by geometric engineering, the refined topological A-model partition function on a local toric Calabi-Yau threefold. We also study the quantum stringy corrections in the stringy instanton partition function which is not captured by the refined topological strings.
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Manabe, M. Stringy instanton counting and topological strings. J. High Energ. Phys. 2015, 97 (2015). https://doi.org/10.1007/JHEP07(2015)097
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DOI: https://doi.org/10.1007/JHEP07(2015)097