Abstract
The soft wall AdS/QCD holographic model provides simple estimates for the spectra of light mesons and glueballs satisfying linear Regge trajectories. It is also an interesting tool to represent the confinement/deconfinement transition of a gauge theory, that is pictured as a Hawking-Page transition from a dual geometry with no horizon to a black hole space. A very interesting tool to analyze stability of general physical systems that are localized in space is the configuration (or complexity) entropy (CE). This quantity, inspired in Shannon information entropy, is defined in terms of the energy density of the system in momentum space. The purpose of this work is to use the CE to investigate the stability of the soft wall background as a function of the temperature. A nontrivial aspect is that the geometry is an anti-de Sitter black hole, that has a singular energy density. In order to make it possible to calculate the CE, we first propose a regularized form for the black hole energy density. Then, calculating the CE, it is observed that its behavior is consistently related to the black hole instability in anti-de Sitter space. Another interesting result that emerges from this analysis is that the regularized energy density shows a behavior similar to the Wien law, satisfied by black body radiation. That means: the momentum kmax where the energy density is maximum, varies with the temperature T obeying the relation: T/kmax=constant in the deconfined phase.
Highlights
It was proposed in [1,2,3] that the configuration entropy (CE) works as an indicator of the stability of physical systems
The Shannon information entropy [4] for a discrete variable with probabilities pn for the possible values that it can assume is defined as: S = − pn log pn
The configuration entropy is defined as a continuous version of (1.1), that for a one-dimensional system reads
Summary
It was proposed in [1,2,3] that the configuration entropy (CE) works as an indicator of the stability of physical systems. The modal fraction can alternatively be defined to be a normalized function, replacing in the denominator of eq (1.3) the square of the maximum value of the energy density in momentum space by |ρ(k)|2dk. Such a definition would be more similar to the Shannon entropy, where the probabilities are normalized, but lead to negative values for the CE. For temperatures T above a critical value Tc the geometry dual to the gauge theory is an AdS black hole, while for T < Tc it is just a thermal AdS space. For an interesting alternative study of deconfinement transition in holographic QCD using entanglement entropy see [35]
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