Approaching the conformal WZW behavior in the infrared limit of two-dimensional massless QCD: A lattice study

Two-dimensional QCD with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>N</a:mi><a:mi>c</a:mi></a:msub></a:math> colors and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>N</c:mi><c:mi>f</c:mi></c:msub></c:math> flavors of massless fermions in the fundamental representation is expected to exhibit conformal behavior in the infrared governed by a <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>u</e:mi><e:mo stretchy="false">(</e:mo><e:msub><e:mi>N</e:mi><e:mi>f</e:mi></e:msub><e:mo stretchy="false">)</e:mo></e:math> Wess–Zumino–Witten model with level <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>N</i:mi><i:mi>c</i:mi></i:msub></i:math>. Using numerical analysis within the lattice formalism with exactly massless overlap fermions, we show the emergence of such behavior in the infrared limit. Both the continuum extrapolated low-lying eigenvalues of the massless Dirac operator and the propagator of scalar mesons exhibit a flow from the ultraviolet to the infrared. We find that the amplitude of the conserved current correlator remains invariant under the flow, while the amplitude of the scalar correlator approaches <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>N</k:mi><k:mi>f</k:mi></k:msub></k:math>-independent values in the infrared. Published by the American Physical Society 2024