# Baryon number current in holographic noncommutative QCD

## TL;DR

This paper studies how noncommutative geometry affects the phase transition related to baryon number current in a holographic QCD model under external fields, revealing that noncommutativity influences transition parameters and phase diagram shape.

## Contribution

It demonstrates that noncommutativity alters the transition temperature and fields in the holographic QCD model without changing the phase structure itself.

## Key findings

- Transition temperature $T_c$ depends on noncommutativity parameter $ heta$
- Shape of the phase diagram is affected by noncommutativity
- Range of $ heta$ is constrained by reality conditions

## Abstract

We consider the noncommutative deformation of the finite temperature holographic QCD (Sakai--Sugimoto) model in external electric and magnetic field and evaluate the effect of the noncommutaivity on the properties of the conductor-insulator phase transition associated with a baryon number current. Although the noncommutative deformation of the gauge theory does not change the phase structure with respect to the baryon number current, the transition temperature $T_{c}$, the transition electric field $e_{c}$ and magnetic field $b_{c}$ in the conductor-insurator phase transition depend on the noncommutativity parameter $\theta$. Namely, the noncommutativity of space coordinates has an influence on the shape of the phase diagram for the conductor-insurator phase transition. On the other hand, the allowed range of the noncommutativity parameter can be restricted by the reality condition of the constants of motion.