Holographic complexity of braneworld in Horndeski gravity

TL;DR

This paper explores how a probe string affects the holographic complexity of a braneworld in Horndeski gravity using the CA conjecture, analyzing the impact of scalar fields and boundary particles on complexity growth.

Contribution

It introduces a numerical analysis of the holographic complexity growth in Horndeski gravity with a probe string, considering scalar field spatial dependence and boundary particle effects.

Findings

Growth rate of complexity depends on scalar field and warp factor

Numerical solutions for warp factor, scalar field, and superpotential are provided

Complexity evolution is analyzed within the WDW patch with null boundaries

Abstract

This work investigates the influence of a probe string on the complexity of braneworld according to the CA (Complexity equals action) conjecture within the Horndeski gravity. In the current study, it is considered that scalar fields that source Horndeski gravity has a spatial dependence. In addition, our system contains a particle moving on the boundary, which corresponds to the insertion of a fundamental string in the higher dimensional bulk. Such an effect is given by the Nambu-Goto term, which also incorporates the time-dependence and evolution in our system. Both warp factor, scalar field, and superpotential values are derived numerically assuming appropriate initial conditions, and the growth rate of holographic complexity is analyzed within the so-called Wheeler-De Witt (WDW) patch with null-like hypersurfaces present.