Neural Ordinary Differential Equations for Mapping the Magnetic QCD Phase Diagram via Holography

TL;DR

This paper introduces a neural ODE-based holographic model to map the QCD phase diagram under magnetic fields, revealing complex phase structures and multiple critical endpoints with variable critical exponents, advancing theoretical predictions for experiments.

Contribution

It develops a novel neural ODE approach to construct holographic QCD models from lattice data, uncovering rich phase structures and multiple CEPs under magnetic fields.

Findings

Identification of two distinct critical endpoints at high magnetic field.

Observation of variable critical exponents depending on CEP location.

Potential violation of scaling relations in strong magnetic fields.

Abstract

The QCD phase diagram is crucial for understanding strongly interacting matter under extreme conditions, with major implications for cosmology, neutron stars, and heavy-ion collisions. We present a novel holographic QCD model utilizing neural ordinary differential equations (ODEs) to map the QCD phase diagram under magnetic field $B$, baryon chemical potential $\mu_B$, and temperature $T$. By solving the inverse problem of constructing a gravitational theory from Lattice QCD data, we reveal an unprecedentedly rich phase structure at finite $B$, including multiple critical endpoints (CEPs) in strong magnetic fields. Specifically, for {$B = 1.618 \, \mathrm{GeV}^2=2.592 \times 10^{19}$ Gauss}, we identify two distinct CEPs at $(T_C = 87.3 \, \mathrm{MeV}, \, \mu_C = 115.9 \, \mathrm{MeV})$ and $(T_C = 78.9 \, \mathrm{MeV}, \, \mu_C = 244.0 \, \mathrm{MeV})$. Notably, the critical exponents vary depending on the CEP's location, and the conventional scaling relations can be violated in the presence of strong magnetic fields. These findings significantly advance our understanding of the QCD phase structure and provide concrete predictions for experimental validation at upcoming facilities such as FAIR, JPARC-HI, and NICA.