  We investigate two dimensional (2d) quantum field theories which exhibit Non-
Lorentzian Ka\v{c}-Moody (NLKM) algebras as their underlying symmetry. Our
investigations encompass both 2d Galilean (speed of light $c \rightarrow
\infty$) and Carrollian ($c \rightarrow 0$) CFTs with additional number of
infinite non-Abelian currents, stemming from an isomorphism between the two
algebras. We alternate between an intrinsic and a limiting analysis. Our NLKM
algebra is constructed first through a contraction and then derived from an
intrinsically Carrollian perspective. We then go on to use the symmetries to
derive a Non-Lorentzian (NL) Sugawara construction and ultimately write down
the NL equivalent of the Knizhnik Zamolodchikov equations. All of these are
also derived from contractions, thus providing a robust cross-check of our
analyses.
