Maps scalar perturbations around extremal charged black holes to Seiberg-Witten quantization to obtain the first non-perturbative quasinormal mode spectrum for charged massive fields.
How instanton combinatorics solves Painlev\'e VI, V and III's
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abstract
We elaborate on a recently conjectured relation of Painlev\'e transcendents and 2D CFT. General solutions of Painlev\'e VI, V and III are expressed in terms of $c=1$ conformal blocks and their irregular limits, AGT-related to instanton partition functions in $\mathcal{N}=2$ supersymmetric gauge theories with $N_f=0,1,2,3,4$. Resulting combinatorial series representations of Painlev\'e functions provide an efficient tool for their numerical computation at finite values of the argument. The series involve sums over bipartitions which in the simplest cases coincide with Gessel expansions of certain Toeplitz determinants. Considered applications include Fredholm determinants of classical integrable kernels, scaled gap probability in the bulk of the GUE, and all-order conformal perturbation theory expansions of correlation functions in the sine-Gordon field theory at the free-fermion point.
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Formal series expansions of accessory parameters in confluent Heun equations are obtained from Voros periods and matched to classical irregular conformal blocks by choosing appropriate cycles on the spectral curve.
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Accessory Parameter of Confluent Heun Equations, Voros Periods and classical irregular conformal blocks
Formal series expansions of accessory parameters in confluent Heun equations are obtained from Voros periods and matched to classical irregular conformal blocks by choosing appropriate cycles on the spectral curve.