Complexity of Einstein-Maxwell-non-minimal coupling $R^2F^2$: the role of the penalty factor

Abstract

We investigate holographic complexity in Einstein-Maxwell theory with a non-minimal coupling of the form $R^2F_{\mu\nu}F^{\mu\nu}$ within the complexity=anything framework. A perturbative AdS black brane solution is constructed to first order in the non-minimal coupling parameter. Owing to the linear temperature dependence of the resistivity, this model provides a holographic realization of strange metal behavior. The complexity growth rate (CGR) is governed by three independent parameters: the conserved charge, the non-minimal coupling, and the choice of the generalized term entering the complexity functional. We consider three representative generalizations, namely the Weyl tensor squared, $R^2F^2$ , and $F^2$. We provide a physical interpretation of these parameters, the generalized bulk functional analytically induces a deformation of the effective cost metric, which can be interpreted as a bulk penalty factor, while the conserved charge and the non-minimal coupling control an effective scrambling time in the dual theory. The role of the generalization parameter is shown to be closely tied to the structure of the corresponding quantum circuit.