Dice Question Streamline Icon: https://streamlinehq.com

Conformal bootstrap for noncompact WZW models and H^3 cosets

Implement the conformal bootstrap for Wess–Zumino–Witten conformal field theories with noncompact target groups or coset spaces such as H^3 = SL(2,C)/SU(2), deriving consistent three-point structure constants and conformal blocks.

Information Square Streamline Icon: https://streamlinehq.com

Background

A probabilistic construction has recently been achieved for a non-linear sigma model with target H3, within the broader family of WZW models. Bootstrap methods are well-developed for compact groups via VOA techniques, but the noncompact case presents substantial challenges.

Extending the bootstrap to noncompact settings would bridge constructive approaches and algebraic structures in a class of physically significant CFTs.

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 7 (Further developments, related results and open problems) — Path integrals for other CFTs