# Twistors, integrability, and 4d Chern-Simons theory

### APA

Bittleston, R. (2021). Twistors, integrability, and 4d Chern-Simons theory. Perimeter Institute. https://pirsa.org/21100050

### MLA

Bittleston, Roland. Twistors, integrability, and 4d Chern-Simons theory. Perimeter Institute, Oct. 29, 2021, https://pirsa.org/21100050

### BibTex

@misc{ pirsa_21100050, doi = {10.48660/21100050}, url = {https://pirsa.org/21100050}, author = {Bittleston, Roland}, keywords = {Mathematical physics}, language = {en}, title = {Twistors, integrability, and 4d Chern-Simons theory}, publisher = {Perimeter Institute}, year = {2021}, month = {oct}, note = {PIRSA:21100050 see, \url{https://pirsa.org}} }

Roland Bittleston Perimeter Institute for Theoretical Physics

## Abstract

I will connect approaches to classical integrable systems via 4d Chern-Simons theory and via symmetry reductions of the anti-self-dual Yang-Mills equations. In particular, I will consider holomorphic Chern-Simons theory on twistor space, defined using a range of meromorphic (3,0)-forms. On shell these are, in most cases, found to agree with actions for anti-self-dual Yang-Mills theory on space-time. Under symmetry reduction, these space-time actions yield actions for 2d integrable systems. On the other hand, performing the symmetry reduction directly on twistor space reduces the holomorphic Chern-Simons action to 4d Chern-Simons theory.

Zoom Link: https://pitp.zoom.us/j/99193672959?pwd=RUJ3N3h2V3RFK3ZNVVVCK1E3bXJ2Zz09