Procházka–Rapčák Feigin–Frenkel duality conjecture for N=2 cosets

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Let n,r,sn,r,s be non-negative integers, and let CN=2ψ(n,r∣s){\mathcal C}^{\psi}_{{\mathcal N}=2}(n,r|s) denote the corresponding N=2 coset vertex algebra. Procházka–Rapčák duality conjecture.

CN=2ψ(n,r∣s)≅{CN=2ψ−1(r−s,n+s∣s),r≥s,CN=2ψ−1(s−r−1,r∣n+r+1),r<s.{\mathcal C}^{\psi}_{{\mathcal N}=2}(n,r|s)\cong\begin{cases}{\mathcal C}_{{\mathcal N}=2}^{\psi^{-1}}(r-s,n+s|s),&r\geq s,\\{\mathcal C}_{{\mathcal N}=2}^{\psi^{-1}}(s-r-1,r|n+r+1),&r<s.\end{cases}

These are conjectured Feigin–Frenkel-type dualities specialized to the universal N=2{\mathcal N}=2 setting; the supplied text gives no resolution evidence.

References

Primary source

Thomas Creutzig, Volodymyr Kovalchuk, Andrew R. Linshaw, Arim Song and Uhi Rinn Suh, “Universal 2-parameter N=2 supersymmetric W_-algebra”, arXiv:2604.20750 (2026).

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