Magnetized Baryonic layer and a novel BPS bound in the gauged-Non-Linear-Sigma-Model-Maxwell theory in (3+1)-dimensions through Hamilton-Jacobi equation

TL;DR

This paper derives a new BPS bound in gauged Non-Linear-Sigma-Model-Maxwell theory using Hamilton-Jacobi methods, revealing stable hadronic layers with quantized surface area and unique charge-flux relations.

Contribution

It introduces a novel BPS bound in (3+1)D gauged NLSM-Maxwell theory, linking topological charge to Baryonic charge via Hamilton-Jacobi equations.

Findings

Derived a saturable BPS bound using Hamilton-Jacobi equation.

Identified hadronic layers with quantized surface area.

Established the relation between magnetic flux and Baryonic charge.

Abstract

It is show that one can derive a novel BPS bound for the gauged Non-Linear-Sigma-Model (NLSM) Maxwell theory in (3+1) dimensions which can actually be saturated. Such novel bound is constructed using Hamilton-Jacobi equation from classical mechanics. The configurations saturating the bound represent Hadronic layers possessing both Baryonic charge and magnetic flux. However, unlike what happens in the more common situations, the topological charge which appears naturally in the BPS bound is a non-linear function of the Baryonic charge. This BPS bound can be saturated when the surface area of the layer is quantized. The far-reaching implications of these results are discussed. In particular, we determine the exact relation between the magnetic flux and the Baryonic charge as well as the critical value of the Baryonic chemical potential beyond which these configurations become thermodynamically unstable.