Holographic complexity of the Klebanov-Strassler background

We study the complexity of the gravity dual to the confining <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>N</a:mi> <a:mo stretchy="false">)</a:mo> <a:mo>×</a:mo> <a:mi>S</a:mi> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>N</a:mi> <a:mo>+</a:mo> <a:mi>M</a:mi> <a:mo stretchy="false">)</a:mo> </a:math> Klebanov-Strassler gauge theory, which is an important test case for holographic complexity in higher-dimensional and nonconformal gauge-gravity dualities. We emphasize the dependence of the complexity on parameters of the gauge theory, finding a common behavior with confinement scale for several complexity functionals. We also analyze how the complexity diverges with the UV cutoff, which is more complicated than in AdS backgrounds because the theory is nonconformal. Our results may provide new perspectives on questions in the holographic complexity program as well as a starting point for further studies of complexity in general gauge-gravity dualities.