PIRSA:24070081 Conference

DOI10.48660/24070081

Conference/School: Celestial Holography Summer School 2024

(2024). Collinear singularities from a double cover of twistor space. Perimeter Institute. https://pirsa.org/24070081

Collinear singularities from a double cover of twistor space. Perimeter Institute, Jul. 24, 2024, https://pirsa.org/24070081 

@misc{ pirsa_PIRSA:24070081,
  doi = {10.48660/24070081},
  url = {https://pirsa.org/24070081},
  author = {},
  keywords = {},
  language = {en},
  title = {Collinear singularities from a double cover of twistor space},
  publisher = {Perimeter Institute},
  year = {2024},
  month = {jul},
  note = {PIRSA:24070081 see, \url{https://pirsa.org}}
}

Abstract

Based on an idea of Kevin Costello, I will show how to construct a double cover of the twistor space of $\mathbb{R}^4$, $X = \pi^*(\mathcal{O}(1)\oplus\mathcal{O}(1))\to\Sigma$ where $\Sigma$ is an (hyper)elliptic curve. I then discuss how holomorphic theories such as BF and Chern-Simons theory on $X$ descend to theories on ordinary twistor space. Once on twistor space, compactifying along the $\mathbb{CP}^1$ direction of twistor space produces a corresponding 4d theory where we can study the algebra of collinear singularities. I will present my calculations which show that this algebra lives on the elliptic curve defining the double cover of twistor space.

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