In the 3D Janus background, defect operator dimensions shift by O(c_J^2), and BOPE coefficients are read off as residues of Heun connection coefficients.
Heun,Zur theorie der riemann’schen functionen zweiter ordnung mit vier verzweigungspunkten, Mathematische Annalen 33 (1888) 161
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Janus correlators and Heun's equation
In the 3D Janus background, defect operator dimensions shift by O(c_J^2), and BOPE coefficients are read off as residues of Heun connection coefficients.