Neural Network Modeling of Heavy-Quark Potential from Holography

TL;DR

This paper develops a neural network-based holographic model for the heavy-quark potential in QCD, accurately reproducing lattice data and providing analytical expressions for finite temperature and chemical potential scenarios.

Contribution

It introduces a novel use of Multi-Layer Perceptrons and Kolmogorov-Arnold Networks to model and analyze the heavy-quark potential holographically, validating and extending existing models.

Findings

MLP accurately reproduces lattice QCD heavy-quark potential.

KAN provides exact analytical reconstruction of the deformation factor.

The combined approach enables analytical modeling at finite temperature and chemical potential.

Abstract

Using Multi-Layer Perceptrons (MLP) and Kolmogorov-Arnold Networks (KAN), we construct a holographic model based on lattice QCD data for the heavy-quark potential in the 2+1 system. The deformation factor $w(r)$ in the metric is obtained using the two types of neural network. First, we numerically obtain $w(r)$ using MLP, accurately reproducing the QCD results of the lattice, and calculate the heavy quark potential at finite temperature and the chemical potential. Subsequently, we employ KAN within the Andreev-Zakharov model for validation purpose, which can analytically reconstruct $w(r)$, matching the Andreev-Zakharov model exactly and confirming the validity of MLP. Finally, we construct an analytical holographic model using KAN and study the heavy-quark potential at finite temperature and chemical potential using the KAN-based holographic model. This work demonstrates the potential of KAN to derive analytical expressions for high-energy physics applications.