Abstract
We construct analytic (3+1)-dimensional Skyrmions living at finite Baryon density in the SU(N) Skyrme model that are not trivial embeddings of SU(2) into SU(N). We used Euler angles decomposition for arbitrary N and the generalized hedgehog Ansatz at finite Baryon density. The Skyrmions of high topological charge that we find represent smooth Baryonic layers whose properties can be computed explicitly. In particular, we determine the energy to Baryon charge ratio for any N showing the smoothness of the large N limit. The closeness to the BPS bound of these configurations can also be analyzed. The energy density profiles of these finite density Skyrmions have \textit{lasagna-like} shape in agreement with recent experimental findings. The shear modulus can be precisely estimated as well and our analytical result is close to recent numerical studies in the literature.
Highlights
The characterization of the phase diagram of the lowenergy limit of QCD at finite baryon density and low temperatures has motivated intense research in the last two decades
Together with the uselessness of perturbation theory at low energy, this means that the complicated phase diagram of low-energy QCD cannot be analyzed with the available analytic techniques
We focus on the analytic computations of relevant physical properties, such as the energy density, the energy per baryon, and the shear modulus of nuclearlasagna-like structures living at finite density
Summary
The characterization of the phase diagram of the lowenergy limit of QCD at finite baryon density and low temperatures has motivated intense research in the last two decades (see Ref. [1] and references therein). In the present case, analytic solutions can disclose relevant physical properties of very complex structures which are difficult to analyze even numerically Until recently, these types of nonhomogeneous condensates in the low-energy limit of QCD in (3 þ 1) dimensions could not be properly understood analytically. A simplified version of the low-energy limit of QCD that encodes many relevant features is the (1 þ 1)-dimensional version of the NJL model, known as the chiral GrossNeveu model [16,17,18,19] Such a model possesses a crystalline phase at low temperature and finite baryon density [20,21,22,23]. We combine the use of Euler angles for SUðNÞ developed in Refs. [39,40,41] together with the use of nonspherical hedgehog ansatz introduced in Refs. [42,43,44,45,46,47,48,49,50]
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