Collinear singularities from a double cover of twistor space

          @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.