Holographic Friedmann Equation and $\cal{N}=$4 SYM theory

TL;DR

This paper explores how the holographic duality relates the bulk Einstein equations to a 4D Friedmann equation, revealing how boundary matter and cosmological constant influence the dynamics of ${ m extbf{N}=4}$ SYM theory and cosmological phenomena.

Contribution

It introduces the concept of holographic Friedmann equations linking bulk gravity to boundary matter effects in ${ m extbf{N}=4}$ SYM theory, providing new insights into cosmological and gauge theory dynamics.

Findings

Boundary matter and cosmological constant control SYM dynamics.

Decoupled matters influence confinement and symmetry breaking.

Results offer implications for cosmological universe development.

Abstract

According to the AdS/CFT correspondence, the ${\cal N}=4$ supersymmetric Yang-Mills (SYM) theory has been studied by solving the dual supergravity. In solving the bulk Einstein equation, we find that it could be related to the 4D Friedmann equation, which is solved by using the cosmological constant and the energy density of the matters on the boundary, and they are dynamically decoupled from the SYM theory. We call this combination of the bulk Einstein equations and the 4D Friedmann equation as holographic Friedmann equations (HFE). Solving the HFE, it is shown how the 4D decoupled matters and the cosmological constant control the dynamical properties of the SYM theory, quark confinement, chiral symmetry breaking, and baryon stability. From their effect on the SYM, the matters are separated to two groups. Our results would give important information in studying the cosmological development of our universe.