Abstract
We continue our study of the semi-classical (large central charge) expansion of the toroidal one-point conformal block in the context of the 2d/4d correspondence. We demonstrate that the Seiberg-Witten curve and (ϵ 1-deformed) differential emerge naturally in conformal field theory when computing the block via null vector decoupling equations. This framework permits us to derive ϵ 1-deformations of the conventional relations governing the prepotential. These enable us to complete the proof of the quasi-modularity of the coefficients of the conformal block in an expansion around large exchanged conformal dimension. We furthermore derive these relations from the semi-classics of exact conformal field theory quantities, such as braiding matrices and the S-move kernel. In the course of our study, we present a new proof of Matone’s relation for \( \mathcal{N} \) = 2* theory.
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ArXiv ePrint: 1404.7378
Unité Mixte du CNRS et de l’ École Normale Supérieure associée à l’Université Pierre et Marie Curie 6, UMR 8549.
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Kashani-Poor, AK., Troost, J. Quantum geometry from the toroidal block. J. High Energ. Phys. 2014, 117 (2014). https://doi.org/10.1007/JHEP08(2014)117
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DOI: https://doi.org/10.1007/JHEP08(2014)117