Crystals of superconducting Baryonic tubes in the low energy limit of QCD at finite density

TL;DR

This paper constructs and analyzes ordered arrays of superconducting Baryonic tubes in low-energy QCD using a Skyrme model, demonstrating their universal properties and stability features across different expansion orders.

Contribution

It introduces an ansatz that reduces complex field equations to a solvable form, enabling analytical construction of Baryonic tube crystals at all orders of the 't Hooft expansion.

Findings

Solutions represent ordered arrays of Baryonic superconducting tubes.

Persistent currents are tied to topological charge and vanish outside the tubes.

Subleading corrections influence stability and Baryon density bounds.

Abstract

The low energy limit of QCD admits (crystals of) superconducting Baryonic tubes at finite density. We begin with the Maxwell-gauged Skyrme model in (3+1)-dimensions (which is the low energy limit of QCD in the leading order of the large N expansion). We construct an ansatz able to reduce the seven coupled field equations in a sector of high Baryonic charge to just one linear Schrodinger-like equation with an effective potential (which can be computed explicitly) periodic in the two spatial directions orthogonal to the axis of the tubes. The solutions represent ordered arrays of Baryonic superconducting tubes as (most of) the Baryonic charge and total energy is concentrated in the tube-shaped regions. They carry a persistent current (which vanishes outside the tubes) even in the limit of vanishing U(1) gauge field: such a current cannot be deformed continuously to zero as it is tied to the topological charge. Then, we discuss the subleading corrections in the 't Hooft expansion to the Skyrme model (called usually \mathcal{L}_{6}$, $\mathcal{L}_{8}$ and so on). Remarkably, the very same ansatz allows to construct analytically these crystals of superconducting Baryonic tubes at any order in the 't Hooft expansion. Thus, no matter how many subleading terms are included, these ordered arrays of gauged solitons are described by the same ansatz and keep their main properties manifesting a universal character. On the other hand, the subleading terms can affect the stability properties of the configurations setting lower bounds on the allowed Baryon density.