Holographic complexity in string and M theory

Thus far, the literature regarding holographic complexity almost entirely focuses on the context of (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>d</a:mi><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math>)-dimensional anti–de Sitter spacetime rather than the full higher-dimensional gauge/gravity duality in string or M theory. We provide a framework to study holographic complexity in the full duality, explaining the relation of complexity functionals in the higher-dimensional theory to those in anti–de Sitter spacetime and when complexity functionals can apply universally to gauge/gravity dualities rather than a specific dual pair. We also show that gauge invariance constrains boundary terms for complexity functionals, using the 10- and 11-dimensional supergravity actions as key examples. Finally, we propose new universal complexity functionals following these considerations, including a revised gauge-invariant action complexity.