Seminar on topological string theory, Spring 2022

Overview

This will be a seminar on topological string theory. The phrase "topological string theory" can mean a few different things, and which direction this seminar proceeds will depend on the interests of the participants. One possible organizing principle for this seminar is the Givental formula for higher-genus Gromov-Witten invariants. This formula has its roots in the origin of the Fukaya category from a topological conformal field theory. We will investigate what a TCFT is and its relation to the string field theory of Zwiebach et al. We will also study the Costello-Li proposal for a solution of the string field theory master equation via the BCOV action coupled to holomorphic Chern-Simons theory.

E-mail me (Ben G.) if you want on the mailing list.

The seminar meets 1pm Thursdays in SC232.

Schedule

Date Speaker Topic
Jan. 27 Benjamin Gammage Introduction and organization
Feb. 3 Benjamin Gammage Topological conformal field theories
Feb. 10 Xujia Chen GW invariants of toric CY3s
Feb. 24 Natalia Pacheco-Tallaj Closed string field theory I
Mar. 3 Benjamin Gammage Givental's Lagrangian cone
Mar. 10-?? -- [Seminar on hiatus]
Apr. ?? Maxim Jeffs Closed string field theory II (à la Caldararu-Tu)
Apr. ?? -- Closed string field theory III: BCOV theory
Apr. ?? -- Open-closed string field theory

References

  1. Zwiebach, Closed string field theory: An introduction
  2. Witten, Chern-Simons gauge theory as a string theory
  3. Givental, Gromov-Witten invariants and quantization of quadratic Hamiltonians
  4. Givental, Symplectic geometry of Frobenius structures
  5. Costello, Topological conformal field theories and Calabi-Yau categories
  6. Lurie, On the classification of topological field theories
  7. Costello, The Gromov-Witten potential associated to a TCFT (Published title: "The partition function of a topological field theory")
  8. Costello-Zwiebach, Hyperbolic string vertices
  9. Costello, Topological conformal field theories and gauge theories
  10. Costello-Li, Twisted supergravity and its quantization
  11. Costello-Li, Quantum BCOV theory on Calabi-Yau manifolds and the higher genus B-model
  12. Neitzke-Vafa, Topological strings and their physical applications
  13. Caldararu-Costello-Tu, Categorical enumerative invariants, I: String vertices
  14. Caldararu-Tu, Categorical enumerative invariants, II: Givental formula
  15. Liu, Gromov-Witten invariants of toric Calabi-Yau threefolds
  16. Kontsevich, Mirror symmetry in dimension 3
Organized by Ben G. (that's me!)