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Conformal bootstrap for WZW models with noncompact groups or cosets

Implement the conformal bootstrap for Wess–Zumino–Witten models in the noncompact group case, including coset targets such as H^3 = SL(2,C)/SU(2), extending beyond the compact-group setting where VOA methods succeed.

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Background

WZW models are central CFTs with fields valued in Lie groups or coset spaces. The bootstrap is established for compact groups using VOA techniques, but noncompact targets, including hyperbolic cosets like H3, present major obstacles.

The authors single out the noncompact case as an open problem, emphasizing the lack of a rigorous bootstrap framework analogous to the compact-group setting.

References

Implementing the conformal bootstrap for WZW models is a success of the VOA approach in the case of compact groups G but the case of noncompact groups, or cosets like $H3$, is an open problem.

— Two Decades of Probabilistic Approach to Liouville Conformal Field Theory (2509.21053 - Rhodes et al., 25 Sep 2025) in Section on Path integrals for other CFTs (Further developments, related results and open problems)