Bridging the Chiral symmetry and Confinement with Singularity

TL;DR

This paper presents a holographic quark model linking chiral symmetry breaking and confinement, revealing a mathematical connection to the bag model and exploring the effects of quark mass on hadron spectra.

Contribution

It introduces a holographic model that maps to the bag model, incorporates quark mass effects via Heun's equation, and uncovers new quantization conditions affecting hadron mass spectra.

Findings

Reproduces linear Regge trajectories for zero quark mass

Identifies higher singularities due to quark mass

Provides exact solutions with new quantization conditions

Abstract

We consider a holographic quark model where the confinement is a consequence of the quark condensate. Surprisingly, the equation of motion of our holographic model can be mapped to the old spin-less bag model. Both models correctly reproduce the linear Regge trajectory of hadrons for zero quark mass. For the case of non-zero quark mass, the model lead us to Heun's equation. The mass term is precisely the origin of the higher singularity, which changes the system behavior drastically. Our result can shed some light on why the chiral transition is so close to the confinement transition. In the massive case, the Schroedinger equation is exactly solvable, but only if a surprising new quantization condition, additional to the energy quantization, is applied.