A rigorous inductive proof that the 5-point Liouville conformal block with a level-2 degenerate insertion can be expressed exactly in terms of one hypergeometric function and its derivative.
Notes on Quasinormal Modes of charged de Sitter Blackholes from Quiver Gauge Theories
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abstract
We give the connection formulae for ordinary differential equations with 5 and 6 (and in principle can be generalized to more) regular singularities from the data of instanton partition functions of quiver gauge theories. We check the consistency of these connection formulae by numerically computing the quasinormal modes (QNMs) of Reissner-Nordstr\"om de Sitter (RN-dS) blackhole. Analytic expressions are obtained for all the families of QNMs, including the photon-sphere modes, dS modes, and near-extremal modes. We also argue that a similar method can be applied to the dS-Kerr-Newman blackhole.
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Exact expressions for the 5-Point Liouville conformal block with a level-two degenerate field insertion
A rigorous inductive proof that the 5-point Liouville conformal block with a level-2 degenerate insertion can be expressed exactly in terms of one hypergeometric function and its derivative.