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Accessory parameters in confluent Heun equations and classical irregular conformal blocks

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arxiv 2101.05715 v1 pith:4X3YCJ5G submitted 2021-01-14 math-ph hep-thmath.CAmath.MP

Accessory parameters in confluent Heun equations and classical irregular conformal blocks

classification math-ph hep-thmath.CAmath.MP
keywords accessoryblocksconfluentconformalheunclassicalequationfunctions
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Classical Virasoro conformal blocks are believed to be directly related to accessory parameters of Floquet type in the Heun equation and some of its confluent versions. We extend this relation to another class of accessory parameter functions that are defined by inverting all-order Bohr-Sommerfeld periods for confluent and biconfluent Heun equation. The relevant conformal blocks involve Nagoya irregular vertex operators of rank 1 and 2 and conjecturally correspond to partition functions of a 4D $\mathcal{N}=2$, $N_f=3$ gauge theory at strong coupling and an Argyres-Douglas theory.

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Cited by 5 Pith papers

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    math-ph 2026-05 unverdicted novelty 6.0

    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.