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

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.

Ordered Patterns of (3+1)-Dimensional Hadronic Gauged Solitons in the Low-Energy Limit of Quantum Chromodynamics at a Finite Baryon Density, Their Magnetic Fields and Novel BPS Bounds

“…Now, we will review a novel strategy for finding BPS bounds, presented in [50], which depends on the possibility of constructing a Hamilton-Jacobi equation from a non-negative energy density, T 00 , which depends on two (or more) scalar degrees of freedom A, B. Suppose we have an energy density of the form:…”

“…The analysis of the coupling between the Dirac equation for quarks and the analytic non-homogeneous Baryonic condensates described previously (and in [50]) is of great interest since it will disclose how the non-homogeneous Baryonic condensates affect the spectrum of the Dirac operator, a task whose relevance is comparable with the importance of the analysis of the Dirac spectrum in an Instanton background.…”

“…A natural question arises: is there any way of obtaining solitonic solutions for this theory, given a convenient choice of Maxwell field, which are topologically stable, as is the case for vortices in critical superconductors? We follow the technique introduced in [50]. Using the metric in (32), the ansatz for the F, H, G profiles reads:…”

“…In this paper, we will describe three analytical approaches to describing non-homogeneous Baryonic condensates both without and with the inclusion of electromagnetic interactions, introduced in references [48][49][50]. These techniques allow us to explicitly compute interesting quantities of these Hadronic condensates of high physical interest (which would be difficult to compute otherwise).…”