Deriving dilaton potential in improved holographic QCD from chiral condensate

TL;DR

This paper develops a data-driven holographic QCD model by deriving the dilaton potential from lattice QCD data of the chiral condensate using machine learning techniques, enabling predictions consistent with lattice results.

Contribution

It introduces a novel method to derive the holographic dilaton potential directly from lattice QCD data through neural ODEs, bridging data and holographic modeling.

Findings

Derived explicit dilaton potential from lattice data.

Predicted string breaking distance consistent with lattice QCD.

Established a machine learning approach for holographic QCD modeling.

Abstract

We derive an explicit form of the dilaton potential in improved holographic QCD (IHQCD) from the QCD lattice data of the chiral condensate as a function of the quark mass. This establishes a data-driven holographic modeling of QCD -- machine learning holographic QCD. The modeling consists of two steps for solving inverse problems. The first inverse problem is to find the emergent bulk geometry consistent with the lattice QCD simulation data at the boundary. We solve this problem with the refinement of neural ordinary differential equation, a machine learning technique. The second inverse problem is to derive a bulk gravity action with a dilaton potential such that its solution is the emergent bulk geometry. We solve this problem at non-zero temperature, and derive the explicit form of the dilaton potential. The dilaton potential determines the bulk action, the Einstein-dilaton system, thus we derive holographically the bulk system from the QCD chiral condensate data. The usefulness of the model is shown in the example of the prediction of the string breaking distance, whose value is found to be consistent with another lattice QCD data.