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It is show that one can derive a novel BPS bound for the gaugedNon-Linear-Sigma-Model (NLSM) Maxwell theory in (3+1) dimensions which canactually be saturated. Such novel bound is constructed using Hamilton-Jacobiequation from classical mechanics. The configurations saturating the boundrepresent Hadronic layers possessing both Baryonic charge and magnetic flux.However, unlike what happens in the more common situations, the topologicalcharge which appears naturally in the BPS bound is a non-linear function of theBaryonic charge. This BPS bound can be saturated when the surface area of thelayer is quantized. The far-reaching implications of these results arediscussed. In particular, we determine the exact relation between the magneticflux and the Baryonic charge as well as the critical value of the Baryonicchemical potential beyond which these configurations become thermodynamicallyunstable.

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