  The auxiliary field sigma model (AFSM) has recently been constructed by Ferko
and Smith as deformations of the principal chiral model by including auxiliary
fields and the potential term given by an arbitrary univariate function. This
AFSM provides an infinite family of integrable sigma models including the
original $T\overline{T}$-deformation and the root $T\overline{T}$-deformation.
In this paper, we propose a 4D Chern-Simons (CS) theory with auxiliary fields.
Then the AFSM is derived from this CS theory with the twist function for the
principal chiral model by imposing appropriate boundary conditions for the
gauge field and auxiliary fields. We also derive the AFSM with the Wess-Zumino
term by deforming the twist function and modifying the boundary conditions.
