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Classical Conformal Blocks and Painleve VI
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Classical Conformal Blocks and Painleve VI
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We study the classical c\to \infty limit of the Virasoro conformal blocks. We point out that the classical limit of the simplest nontrivial null-vector decoupling equation on a sphere leads to the Painleve VI equation. This gives the explicit representation of generic four-point classical conformal block in terms of the regularized action evaluated on certain solution of the Painleve VI equation. As a simple consequence, the monodromy problem of the Heun equation is related to the connection problem for the Painleve VI.
Forward citations
Cited by 6 Pith papers
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Projecting Gravitational Fluctuations onto Near-Horizon Throats
A pair of coordinate changes projects Heun-type gravitational fluctuation equations onto two matched hypergeometric problems, reproducing instanton-counting results and yielding Schwarzian zero modes.
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Quasinormal-mode frequencies of extremal Reissner-Nordström black holes for charged and massive scalar fields are computed through Seiberg-Witten/Nekrasov-Shatashvili quantization.
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