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 (epsilon1-deformed) differential emerge naturally in conformal field theory when computing the block via null vector decoupling equations. This framework permits us to derive epsilon1-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=2* theory.

27 pages, 1 figure

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Cited by in corpus (4)

• Non-Perturbative Quantum Geometry II
• Chiral observables and S-duality in N = 2* U(N) gauge theories
• Exact partition functions for the $\Omega$-deformed $\mathcal{N}=2^{\ast }$ $SU(2)$ gauge theory
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours