Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I

By J. Teschner. 2010

172 citations recorded by the source corpus.

We discuss the relation between Liouville theory and the Hitchin integrable system, which can be seen in two ways as a two step process involving quantization and hyperkaehler rotation. The modular duality of Liouville theory and the relation between Liouville theory and the SL(2)-WZNW-model give a new perspective on the geometric Langlands correspondence and on its relation to conformal field theory.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5657b180935d96edf8087062168181c796bac4ac

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. C. Vafa
2. Mina Aganagic
3. R. Dijkgraaf
4. Marcos Mariño
5. Yuji Tachikawa
6. Miranda C. N. Cheng
7. J. Teschner
8. H. Kanno

In Nuclear and High Energy Physics

1. C. Vafa
2. Marcos Mariño
3. Mina Aganagic
4. R. Dijkgraaf
5. H. Kanno
6. Yuji Tachikawa
7. Sergei Gukov
8. A. Klemm

In Statistical and Nonlinear Physics

1. Mina Aganagic
2. C. Vafa
3. R. Dijkgraaf
4. Marcos Mariño
5. Yuji Tachikawa
6. Miranda C. N. Cheng
7. L. Alday
8. Daniel Krefl

Citations in the corpus

• Affine SL(2) Conformal Blocks from 4d Gauge Theories (2010, background): “While preparing this manuscript, [17] appeared, which overlaps with Sec.”
• Quantum geometry of refined topological strings (2011, background): “A related observation that the gauge theory instanton partition function in the presence of the surface operator becomes in the NS limit the eigenfunction of the Hamiltonians of the corresponding quantum integrable systems has been previously made in [12, 14, 50, 51].”
• Instanton counting with a surface operator and the chain-saw quiver (2011, background): “two points of view should be related to the mapping between the Toda theory and the WZW theory [74, 75, 76, 77, 78], and is also worth further investigation.”
• Chern-Simons theory and S-duality (2011, unknown): “Conjecturally, this problem is equivalent to the quantization of the Teichmüller space [15, 57], thus, justifying one of the key relations HLiouv b (C) = HN=2 1,2 (S3) in the AGT correspondence, cf.”
• Isomonodromic Tau-Functions from Liouville Conformal Blocks (2014, background): “the null-vector decouplingequations in Liouville theory yields Hamilton-Jacobi - like equations that define the Hamiltonians generating the isomonodromic deformation flows. This was first pointed out in [T11], a speci al case was later rediscovered in [LLNZ]. It seems remarkable that there exist relati”