nLab quantum Teichmüller theory

Idea

Quantum Teichnüller theory studies a deformation quantization of Teichmüller space.

According to a conjecture in (Verlinde 90) the corresponding Hilbert space may be identified with the space of conformal blocks of Liouville theory.

References

The conjectured relation to Liouville theory is due to

• Herman Verlinde, Conformal field theory, two-dimensional quantum gravity and quantization of Teichmüller space. Nuclear Physics B 337.3 (1990): 652-680.

A review is in section 2 of

• Dylan Allegretti, Notes on Quantum Teichmüller theory (pdf)