## Quantum geometry from the toroidal block

### 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 N $$\mathcal{N}$$ = 2* theory

Year: 2014
DOI identifier: 10.1007/JHEP08(2014)117
OAI identifier: oai:www.openaccessrepository.it:8410

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