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Analytic properties of the Virasoro modular kernel · Around

2016

Analytic properties of the Virasoro modular kernel

Nemkov, Nikita

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On the space of generic conformal blocks the modular transformation of the underlying surface is realized as a linear integral transformation.

We show that the analytic properties of conformal block implied by Zamolodchikov's formula are shared by the kernel of the modular transformation and illustrate this by explicit computation in the case of the one-point toric conformal block.

Built on

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Al. Zamolodchikov, “Conformal symmetry in two dimensions: an explicit recurrence formula for the conformal partial wave amplitude,” Commun.Math.Phys
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Al. Zamolodchikov, “Conformal symmetry in two-dimensional space: Recursion representation of conformal block,” Theor.Math.Phys
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N. Wyllard, “A(N-1) conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories,” JHEP
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R. Poghossian, “Recursion relations in CFT and N=2 SYM theory,” JHEP
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2012

Cited alongside, same era.

M. Billo, M. Frau, L. Gallot, A. Lerda, and I. Pesando, “Modular anomaly equation, heat kernel and S-duality in N = 2 N=2 theories,” JHEP

2013

Cited alongside, same era.

J. Teschner, “From Liouville theory to the quantum geometry of Riemann surfaces,” arXiv:hep-th/0308031 [hep-th]

Cited in the paper.

N. Nemkov, “On fusion kernel in Liouville theory,” arXiv:1409.3537 [hep-th]

Cited in the paper.

2015

Later among the works it cites.