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.
|Titolo:||Twistorial topological strings and a tt* geometry for N =2 theories in 4d|
|Autori:||Cecotti S.; Neitzke A.; Vafa C.|
|Rivista:||ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS|
|Data di pubblicazione:||2016|
|Digital Object Identifier (DOI):||10.4310/ATMP.2016.v20.n2.a1|
|Appare nelle tipologie:||1.1 Journal article|