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.

中文翻译：

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超弦可积性的Chern-Simons起源

我们得出 ${\mathrm{广告}}_5\times {\mathrm{小号}}^5$二维Beltrami-Chern-Simons理论中的Green-Schwarz超弦在具有奇异边界条件的流形上还原。在这种构造中，可积分超弦的Lax连接和频谱参数在四个维度上具有简单的几何原点，即规范连接和归约坐标。$\kappa$对称性是由一类奇异规范转换引起的，而世界表度量标准则来自于变化复杂结构的Beltrami微分。我们的方法提供了使用传统场论方法研究可积分全息术的可能性。