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Vertex Algebra constructions for (analytic) Geometric Langlands in genus zero

Davide Gaiotto

Abstract

We employ two-dimensional chiral algebra techniques to produce solutions of certain differential and integral equations which occur in the context of the Analytic Geometric Langlands Program.

Vertex Algebra constructions for (analytic) Geometric Langlands in genus zero

Abstract

We employ two-dimensional chiral algebra techniques to produce solutions of certain differential and integral equations which occur in the context of the Analytic Geometric Langlands Program.

Paper Structure

This paper contains 23 sections, 104 equations.

Table of Contents

  1. Introduction
  2. The non-chiral kernels
  3. Hecke operators intertwining relations
  4. General weights
  5. Generalizations
  6. Structure of the paper
  7. Symplectic bosons
  8. Action, currents, genus $0$ correlation functions, non-chiral theory.
  9. Vertex operators in the Neveu-Schwarz sector
  10. Sub-algebra primaries
  11. Weighed powers
  12. Ramond vertex operators
  13. An example of Ramond correlation functions
  14. Spectral flow
  15. Boundary conditions
  16. ...and 8 more sections