Complexity Growth in Flavor-Dependent Systems

TL;DR

This paper studies how holographic complexity evolves in a flavor-dependent Einstein-Maxwell-Dilaton model, revealing its sensitivity to phase transitions and thermodynamic parameters, with implications for understanding QCD-like systems.

Contribution

It introduces a holographic complexity analysis using the CA conjecture in a flavor-dependent EMD model fitted to lattice QCD data, highlighting complexity's role as a phase transition probe.

Findings

Maximum complexity growth occurs for stationary strings.

Complexity growth decreases with increasing string velocity.

Complexity behavior indicates phase transition types.

Abstract

In this work, we investigate holographic complexity growth in a flavor-dependent Einstein-Maxwell-Dilaton (EMD) model, where the parameters are determined through machine learning algorithms fitted to lattice QCD equation of state (EoS) and baryon number susceptibility data. Within the Complexity=Action (CA) conjecture, we introduce a probe string into the bulk geometry and evaluate the time derivative of its Nambu-Goto (NG) action on the Wheeler-DeWitt (WDW) patch as the holographic dual of complexity growth. Our analysis explores the dependence of complexity growth on string velocity, chemical potential, temperature, and the number of flavors. Results show maximum complexity growth for stationary strings, decreasing with string velocity. At zero chemical potential, complexity growth is largest in the pure gluon system and reduces with the addition of quark flavors. Increasing temperature and chemical potential consistently enhance complexity growth. Furthermore, complexity growth exhibits multi-valued behavior in regions corresponding to first-order transitions and single-valued behavior in crossover regimes, indicating that complexity can serve as a probe for phase transitions.