Flavor dependence of chiral symmetry breaking and the conformal window

We investigate the phase structure of QCD in the vacuum as a function of quark flavor number <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>N</a:mi> <a:mi>f</a:mi> </a:msub> </a:math> within the chiral limit. By self-consistently solving the coupled Dyson-Schwinger equations for the quark and gluon propagators in a minimal QCD scheme, we elucidate the nonperturbative dynamics governing dynamical chiral symmetry breaking. Our calculations determine a critical flavor number of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msubsup> <c:mi>N</c:mi> <c:mi>f</c:mi> <c:mi>c</c:mi> </c:msubsup> <c:mo>=</c:mo> <c:mn>6.81</c:mn> </c:math> which marks the chiral symmetry restoration of quarks. Further analysis reveals the critical exponents of the chiral condensate as <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:mo>−</e:mo> <e:mo stretchy="false">⟨</e:mo> <e:mover accent="true"> <e:mrow> <e:mi>ψ</e:mi> </e:mrow> <e:mrow> <e:mo stretchy="false">¯</e:mo> </e:mrow> </e:mover> <e:mi>ψ</e:mi> <e:mo stretchy="false">⟩</e:mo> <e:mo>∼</e:mo> <e:mo stretchy="false">|</e:mo> <e:msub> <e:mrow> <e:mi>N</e:mi> </e:mrow> <e:mrow> <e:mi>f</e:mi> </e:mrow> </e:msub> <e:mo>−</e:mo> <e:msubsup> <e:mrow> <e:mi>N</e:mi> </e:mrow> <e:mrow> <e:mi>f</e:mi> </e:mrow> <e:mrow> <e:mi>c</e:mi> </e:mrow> </e:msubsup> <e:msup> <e:mrow> <e:mo stretchy="false">|</e:mo> </e:mrow> <e:mrow> <e:mn>0.53</e:mn> <e:mo stretchy="false">(</e:mo> <e:mn>9</e:mn> <e:mo stretchy="false">)</e:mo> </e:mrow> </e:msup> </e:mrow> </e:math> , characterized the second order feature of this phase transition of chiral symmetry. Additionally, we discuss the implications for the walking regime towards the conformal window at larger flavor.