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Non-Abelian Toda field theories from a 4D Chern-Simons theory

We derive non-abelian Toda field theories (NATFTs) from a 4d Chern-Simons (CS) theory with two order defects by employing a certain asymptotic boundary condition. The 4d CS theory is characterized by a meromorphic 1-form $ω$\,. We adopt $ω$ with two simple poles and no zeros, and each of the order defects is located at each pole. As a result, an anisotropy parameter $β^2$ can be identified with the distance between the two defects. As examples, we can derive the (complex) sine-Gordon model and the Liouville theory.