Lectures on the Langlands program and conformal field theory

By E. Frenkel. 2005

241 citations recorded by the source corpus.

These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric reformulation, addressed primarily to physicists. I tried to make it as self-contained as possible, requiring very little mathematical background. Next, we describe the connections between the Langlands Program and two-dimensional conformal field theory that have been found in the last few years. These connections give us important insights into the physical implications of the Langlands duality.

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

View Paper: https://www.semanticscholar.org/paper/0b8d146f81172378d922ac851bac7436dda48b0b

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In Mathematical Physics

1. D. Gaiotto
2. Sergei Gukov
3. E. Witten
4. Tudor Dimofte
5. J. Teschner
6. Branko Dragovich
7. Igor V. Volovich
8. A. Khrennikov

In Nuclear and High Energy Physics

1. Sergei Gukov
2. D. Gaiotto
3. E. Witten
4. Tudor Dimofte
5. Yuji Tachikawa
6. J. Teschner
7. Vasily Pestun
8. N. Seiberg

In Statistical and Nonlinear Physics

1. D. Gaiotto
2. Sergei Gukov
3. E. Witten
4. Yuji Tachikawa
5. J. Teschner
6. Vasily Pestun
7. Sergei V. Kozyrev
8. A. Khrennikov

Citations in the corpus

• Fivebranes and Knots (2011, background): “Geometric Langlands duality (for a review, see [62]) has a generalization, sometimes called quantum geometric Langlands in the mathematics literature, involving a parameter that was called Ψ in [63].”
• Gauge Theory, Ramification, And The Geometric Langlands Program (2006, background): “Additional explanation and references can be found in the introduction to [8] and in a recent review article [ 9 ].”
• p-Adic mathematical physics: the first 30 years (2017, background): “Therefore it can be viewed as part of the Langlands program in number theory and the representation theory [287] (for a recent consideration of the geometrical Langlands program see [292]).”
• Quiver W-algebras (2015, background): “For a survey of duality of W-algebras and its connection with the geometric Langlands program see [1] and [13] section 8.”
• Knot Invariants from Four-Dimensional Gauge Theory (2011, background): “See for example [62] for an explanation of the role of opers in the geometric Langlands correspondence.”
• Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I (2010, methodology): “We refer to [24] for more discussion of the Hecke functors”
• Electric-Magnetic Duality And The Geometric Langlands Program (2006, unknown): “For a recent accessible review see [1].”