Confining potential in holographic bottom-up QCD from WKB

TL;DR

This paper introduces a method using RKR formulas to derive a confining potential in holographic QCD from spectral data, exemplified by vector meson spectra, and analyzes its physical properties.

Contribution

It presents a novel inverse Schrödinger approach to construct bottom-up confining potentials directly from spectral data in holographic QCD.

Findings

Derived a confining potential resembling the hardwall model

Analyzed the thermal deconfinement phase transition

Computed the $ ho$ radial Regge trajectory and configurational entropy

Abstract

By using the \emph{Rydberg--Klein--Rees} (RKR) formulas to solve the inverse Schr\"{o}dinger problem, we found a confining bottom-up potential from a given eigenvalue spectrum. To illustrate this methodology, we consider the vector meson spectrum derived in the D3/D7 system as input data to derive the corresponding bottom-up confining potential that resembles the geometric structure of the so-called hardwall model. We compute some properties for this new bottom-up model, including the thermal deconfinement phase transition, the $\rho$ radial Regge trajectory, and the configurational entropy.