# Quantization of moduli spaces of flat connections and Liouville theory

@article{Teschner2014QuantizationOM, title={Quantization of moduli spaces of flat connections and Liouville theory}, author={J{\"o}rg Teschner}, journal={arXiv: Mathematical Physics}, year={2014} }

We review known results on the relations between conformal field theory, the quantization of moduli spaces of flat PSL(2,R)-connections on Riemann surfaces, and the quantum Teichmueller theory.

## 17 Citations

### Gluing theory of Riemann surfaces and Liouville conformal field theory

- Mathematics
- 2017

We study the gluing theory of Riemann surfaces using formal algebraic geometry, and give computable relations between the associated parameters for different gluing processes. As its application to…

### Quantisation of Super Teichmüller Theory

- Mathematics
- 2015

We construct a quantisation of the Teichmüller spaces of super Riemann surfaces using coordinates associated to ideal triangulations of super Riemann surfaces. A new feature is the non-trivial…

### Confluent conformal blocks of the second kind

- Mathematics
- 2020

We construct confluent conformal blocks of the second kind of the Virasoro algebra. We also construct the Stokes transformations which map such blocks in one Stokes sector to another. In the BPZ…

### Higher complex structures and higher Teichmüller theory

- Mathematics
- 2020

In this PhD thesis, we give a new geometric approach to higher Teichmuller theory. In particular we construct a geometric structure on surfaces, generalizing the complex structure, and we explore its…

### On a canonical quantization of 3D Anti de Sitter pure gravity

- Mathematics
- 2015

A bstractWe perform a canonical quantization of pure gravity on AdS3 using as a technical tool its equivalence at the classical level with a Chern-Simons theory with gauge group SL2ℝ×SL2ℝ$$…

### $\operatorname{SL}(2,\mathbb{C})$ Chern-Simons theory, flat connections, and four-dimensional quantum geometry

- MathematicsAdvances in Theoretical and Mathematical Physics
- 2019

The present paper analyze SL(2,C) Chern-Simons theory on a class of graph complement 3- manifolds, and its relation with classical and quantum geometries on 4-dimensional manifolds. In classical…

### A slow review of the AGT correspondence

- Mathematics
- 2020

Starting with a gentle approach to the AGT correspondence from its 6d origin, these notes provide a wide survey of the literature on numerous extensions of the correspondence. This is the writeup of…

### Teichmüller TQFT vs. Chern-Simons theory

- Mathematics
- 2017

A bstractTeichmüller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2, ℝ) Chern-Simons theory. To…

### On the Relation between Quantized Teichmüller Spaces and the Free Field Quantization of Liouville Theory

- Mathematics
- 2016

We investigate how the quantum Teichmuller theory is encoded in the free field quantization of Liouville theory. We show that the 4-point conformal blocks of Liouville theory contain the eigenstates…

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