Chern-Simons Origin of Superstring Integrability

We derive the ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ Green-Schwarz superstring from four-dimensional Beltrami-Chern-Simons theory reduced on a manifold with singular boundary conditions. In this construction, the Lax connection and spectral parameter of the integrable superstring have a simple geometric origin in four dimensions as gauge connection and reduction coordinate. $\kappa$ symmetry arises as a certain class of singular gauge transformations, while the world-sheet metric comes from complex-structure-changing Beltrami differentials. Our approach offers the possibility of investigating integrable holography using traditional field theory methods.