Asymptotic gauge symmetry and UV extension of the nonperturbative coupling in holographic QCD

We extend our recent analytic study of the strong coupling <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>α</a:mi> <a:mi>eff</a:mi> </a:msub> </a:math> in the nonperturbative and near-perturbative regimes [] by imposing rigorous renormalization-group constraints from asymptotically free gauge theories at <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msup> <c:mi>Q</c:mi> <c:mn>2</c:mn> </c:msup> <c:mo stretchy="false">→</c:mo> <c:mi>∞</c:mi> </c:math> . The asymptotic boundary conditions modify the scaling properties of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msub> <f:mi>α</f:mi> <f:mi>eff</f:mi> </f:msub> </f:math> at large values of the momentum transfer <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msup> <h:mi>Q</h:mi> <h:mn>2</h:mn> </h:msup> </h:math> and lead to a scale-dependent confinement strength <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi>κ</j:mi> <j:mo stretchy="false">(</j:mo> <j:msup> <j:mi>Q</j:mi> <j:mn>2</j:mn> </j:msup> <j:mo stretchy="false">)</j:mo> </j:math> . This requires that both <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>κ</n:mi> <n:mo stretchy="false">(</n:mo> <n:msup> <n:mi>Q</n:mi> <n:mn>2</n:mn> </n:msup> <n:mo stretchy="false">)</n:mo> </n:math> and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:msub> <r:mi>α</r:mi> <r:mi>eff</r:mi> </r:msub> <r:mrow> <r:mo stretchy="false">(</r:mo> <r:msup> <r:mi>Q</r:mi> <r:mn>2</r:mn> </r:msup> <r:mo>,</r:mo> <r:mi>κ</r:mi> <r:mo stretchy="false">(</r:mo> <r:msup> <r:mi>Q</r:mi> <r:mn>2</r:mn> </r:msup> <r:mo stretchy="false">)</r:mo> <r:mo stretchy="false">)</r:mo> </r:mrow> </r:math> remain holomorphic in the complex <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msup> <x:mi>Q</x:mi> <x:mn>2</x:mn> </x:msup> </x:math> plane, except at the physical cuts associated with the heavy-quark thresholds and the singularity flow trajectory studied in our previous Letter. For color SU(3), a precise connection is found between the scaling exponent of <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mi>κ</z:mi> <z:mo stretchy="false">(</z:mo> <z:msup> <z:mi>Q</z:mi> <z:mn>2</z:mn> </z:msup> <z:mo stretchy="false">)</z:mo> </z:math> in the ultraviolet, the value of the infrared fixed point of the strong coupling, and the number of flavors in agreement with observations. The nonperturbative analytic model gives an accurate description of the strong coupling across all scales, up to the highest available data.