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

Abstract

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.

3-dimensional mixed BF theory and Hitchin's integrable system

“…The 4-dimensional gauge theoretic origin of 2-dimensional integrable field theories, as proposed by Costello and Yamazaki in [CY], has been extensively studied over the past couple of years, see for instance [DLMV3,Sc1,FSY1,FSY2,CS,T,THC,BSV,BS,LV,CSV,FSY3,ABW,FSY4,D,St,Sc2,L2,FSY5].…”

3-Dimensional mixed BF theory and Hitchin’s integrable system

“…Each ' * ' denotes a possibly non-zero block matrix. The matrix(36) is invertible since the blocks in position (1, 2), (2, 1) and(3,3) are all invertible by design. Its inverse is then schematically of the block form…”