Bridging the Chiral symmetry and Confinement with Singularity

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.