  We study the chiral limit of 2d QCD with a single quark flavor at finite
$N_c$ using LCT. By modifying the LCT basis according to the quark mass in a
manner motivated by 't Hooft's analysis, we are able to restore convergence for
quark masses much smaller than the QCD strong coupling scale. For such small
quark masses, the IR of the theory is expected to be well described by the
Sine-Gordon model. We verify that LCT numerics are able to capture in detail
the spectrum and correlation functions of the Sine-Gordon model. This opens up
the possibility for studying deformations of various integrable CFTs using LCT
by considering the chiral limit of QCD like theories.
