It is well understood how the 2d free scalar CFT emerges from 3d Chern-Simons theory with chiral boundary conditions. Adapting a recent proposal of Costello and Stefanski, I will show how bosonic string theory can be obtained from this description by coupling to a dynamical Beltrami differential in the 3d theory. In particular, I will show how this Beltrami differential restores worldsheet diffeomorphism and Weyl invariance in the 2d theory, and recover the Polyakov action explicitly. By rewriting the theory in the BV formalism, I will show how the bc ghost system arises from the 3d perspective. Finally, if there is sufficient time, I will provide the 3d realization of vertex operators. This talk is based on work in progress with Kevin Costello and Bogdan Stefanski. ----------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

Costello, Witten, and Yamazaki have recently proposed a new description of quantum integrable systems using a variant of Chern-Simons theory defined on the product of a two dimensional real manifold and a Riemann surface. I'll review their work, and show how to extend it to describe integrable systems with boundary. In particular I'll discuss how it can be used to generate solutions of the boundary Yang-Baxter equation, and how to realise twisted Yangians in the theory. If there is enough time I will explore the result of applying this construction when the Riemann surface is chosen to be a torus.