Continuous quiver gauge theories

We consider half-BPS Wilson loops in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="script">N</a:mi><a:mo>=</a:mo><a:mn>2</a:mn></a:math> long circular quiver gauge theories at large <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>N</d:mi></d:math> with continuous limit shape of ’t Hooft couplings. In the limit of an infinite number of nodes <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>L</f:mi></f:math>, the solution to the localization matrix model is given by Wigner semicircles for any profile of couplings. Higher-order corrections in <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mn>1</h:mn><h:mo>/</h:mo><h:mi>L</h:mi></h:math> can be calculated iteratively. Combining large <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>L</j:mi></j:math> with a strong coupling regime, we identify a double scaling limit that describes dynamics along a fifth dimension, which emerges dynamically from the quiver diagram. We solve the resulting integro-differential equation exactly for a certain range of parameters.