We define twistorial topological strings by considering tt* geometry of the 4d N =2 supersymmetric theories on the Nekrasov- Shatashvili 1/2Ω background, which leads to quantization of the associated hyperKähler geometries. We show that in one limit it reduces to the refined topological string amplitude. In another limit it is a solution to a quantum Riemann-Hilbert problem involving quantum Kontsevich-Soibelman operators. In a further limit it encodes the hyperKähler integrable systems studied by GMN. In the context of AGT conjecture, this perspective leads to a twistorial extension of Toda. The 2d index of the 1/2Ω theory leads to the recently introduced index for N =2 theories in 4d. The twistorial topological string can alternatively be viewed, using the work of Nekrasov-Witten, as studying the vacuum geometry of 4d N =2 supersymmetric theories on T2 × I where I is an interval with specific boundary conditions at the two ends.

Twistorial topological strings and a tt* geometry for N =2 theories in 4d

Cecotti, Sergio;
2016-01-01

Abstract

We define twistorial topological strings by considering tt* geometry of the 4d N =2 supersymmetric theories on the Nekrasov- Shatashvili 1/2Ω background, which leads to quantization of the associated hyperKähler geometries. We show that in one limit it reduces to the refined topological string amplitude. In another limit it is a solution to a quantum Riemann-Hilbert problem involving quantum Kontsevich-Soibelman operators. In a further limit it encodes the hyperKähler integrable systems studied by GMN. In the context of AGT conjecture, this perspective leads to a twistorial extension of Toda. The 2d index of the 1/2Ω theory leads to the recently introduced index for N =2 theories in 4d. The twistorial topological string can alternatively be viewed, using the work of Nekrasov-Witten, as studying the vacuum geometry of 4d N =2 supersymmetric theories on T2 × I where I is an interval with specific boundary conditions at the two ends.
2016
20
2
193
312
https://arxiv.org/abs/1412.4793v1
Cecotti, Sergio; Neitzke, A.; Vafa, C.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/11834
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