Holographic complexity of black non-susy D3-brane and the high temperature limit

TL;DR

This paper investigates the holographic complexity of a non-susy D3-brane and its high temperature limit, revealing that it scales similarly to entanglement entropy and exhibits a crossover to thermal behavior, with parallels in super Yang-Mills theory.

Contribution

It provides the first detailed analysis of the high temperature behavior of holographic complexity for non-susy D3-branes and compares it with super Yang-Mills results.

Findings

Complexity difference scales with temperature similarly to entanglement entropy.

High temperature limit shows crossover to thermal complexity.

Similar behavior observed in super Yang-Mills theory.

Abstract

The holographic complexity of a `black' non-susy $D3$-brane is computed. The difference in the holographic complexity between this geometry in the Fefferman-Graham coordinates and that of the $AdS_5$ geometry is obtained for a strip type subsystem. This is then related to the changes in the energy and the entanglement entropy of the system. We next take the high temperature limit of the change in complexity and observe that it scales with the temperature in the same way as the holographic entanglement entropy. The crossover of the holographic complexity to its corresponding thermal counterpart is similar to the corresponding crossover of the holographic entanglement entropy in the high temperature limit. We further repeat the analysis for $\mathcal{N} =4$ super Yang-Mills theory and observe a similar behaviour.