The Holographic Complexity on Extremal Branes with Exceptional Higher Derivative Interactions

The philosophy of presented multiversum doctrina dominum article is related to the coloring of the theoretical framework with respect to holographic complexity on extremal branes in exclusive higher-dimensional representations. We examine holographic complexity in the doubly holographic model introduced in the current literature to study quantum extremal islands. We focus on the holographic complexity volume proposal for boundary subregions in the island phase. Exploiting the Fefferman-Graham expansion of the metric and other geometric quantities near the extremal brane, we derive the leading contributions to the complexity and interpret these in terms of the generalized volume of the island derived from the induced higher-curvature gravity action on the extremal brane. We discuss the interpretation of path integral optimization as a uniformization problem in even dimensions. This perspective allows for a systematical construction of the higher-dimensional path integral complexity in holographic conformal field theories in terms of Q-curvature actions. Motivated by the exceptional results , we propose a generalization of the higher-dimensional derivative actions of exotic extremal branes.