Analytic non-Abelian gravitating solitons in the Einstein-Yang-Mills-Higgs theory and transitions between them

Two analytic examples of globally regular non-Abelian gravitating solitons in the Einstein-Yang-Mills-Higgs theory in (3+1)-dimensions are presented. In both cases, the space-time geometries are of the Nariai type and the Yang-Mills field is completely regular and of meron type (namely, proportional to a pure gauge). However, while in the first family (type I) $X_{0} = 1/2$ (as in all the known examples of merons available so far) and the Higgs field is trivial, in the second family (type II) $X_{0}$ is not 1/2 and the Higgs field is non-trivial. We compare the entropies of type I and type II families determining when type II solitons are favored over type I solitons: the VEV of the Higgs field plays a crucial role in determining the phases of the system. The Klein-Gordon equation for test scalar fields coupled to the non-Abelian fields of the gravitating solitons can be written as the sum of a two-dimensional DAlembert operator plus a Hamiltonian which has been proposed in the literature to describe the four-dimensional Quantum Hall Effect (QHE): the difference between type I and type II solutions manifest itself in a difference between the degeneracies of the corresponding energy levels.

Analytic multi-Baryonic solutions in the SU(N)-Skyrme model at finite density and a novel transition

We construct explicit analytic solutions of the $SU(N)$-Skyrme model (for generic $N$) suitable to describe different phases of nuclear pasta at finite volume in $(3+1)$ dimensions. The first type are crystals of Baryonic tubes (nuclear spaghetti) while the second type are smooth Baryonic layers (nuclear lasagna). Both the ansatz for the spaghetti and the ansatz for the lasagna phases reduce the complete set of Skyrme field equations to just one integrable equation for the profile within sectors of arbitrary high topological charge. We compute explicitly the total energy of both configurations in terms of the flavor number, the density and the Baryonic charge. Remarkably, our analytic results disclose a novel finite-density transition arising from the competition between the nuclear spaghetti and lasagna phases. Well within the range of validity of the model, one can see that the lasagna phase is energetically favored at high density while the spaghetti is favored at low density. Finally, we briefly discuss the large $N$ limit of our configurations.

Crystals of gauged solitons, force free plasma and resurgence

We show that the (3+1)-dimensional gauged non-linear sigma model minimally coupled to a U(1) gauge field possesses analytic solutions representing gauged solitons at finite Baryon density whose electromagnetic field is a Force Free Plasma. These gauged solitons manifest a crystalline structure and generate in a very natural way persistent currents able to support Force Free Plasma electromagnetic fields. The trajectories of charged test particles moving within these configurations can be characterized. Quite surprisingly, despite the non-integrable nature of the theory, some of the perturbations of these gauged solitons allow to identify a proper resurgent parameter. In particular, the perturbations of the solitons profile are related to the Lame operator. On the other hand, the electromagnetic perturbations on the configurations satisfy a two-dimensional effective Schrodinger equation, where the soliton background interacts with the electromagnetic perturbations through an effective two-dimensional periodic potential. We studied numerically the band energy spectrum for different values of the free parameters of the theory and we found that bands-gaps are modulated by the potential strength. Finally we compare our crystal solutions with those of the (1+1)- dimesional Gross-Neveu model.

General Relativity from Einstein-Gauss-Bonnet gravity

In this work we show that Einstein gravity in four dimensions can be consistently obtained from the compactification of a generic higher curvature Lovelock theory in dimension $D=4+p$, being $pgeq1$. The compactification is performed on a direct product space $mathcal{M}_D=mathcal{M}_4timesmathcal{K}^p$, where $mathcal{K}^p$ is a Euclidean internal manifold of constant curvature. The process is carried out in such a way that no fine tuning between the coupling constants is needed. The compactification requires to dress the internal manifold with the flux of suitable $p$-forms whose field strengths are proportional to the volume form of the internal space. We explicitly compactify Einstein-Gauss-Bonnet theory from dimension six to Einstein theory in dimension four and sketch out a similar procedure for this compactification to take place starting from dimension five. Several black string/p-branes solutions are constructed, among which, a five dimensional asymptotically flat black string composed of a Schwarzschild black hole on the brane is particularly interesting. Finally, the thermodynamic of the solutions is described and we find that the consistent compactification modifies the entropy by including a constant term, which may induce a departure from the usual behavior of the Hawking-Page phase transition. New scenarios are possible in which large black holes dominate the canonical ensamble for all temperatures above the minimal value.

Exact textit{pp}-waves, (A)dS waves and Kundt spaces in the Abelian-Higgs model

We find new exact solutions of the Abelian-Higgs model coupled to General Relativity, characterized by a non-vanishing superconducting current. The solutions correspond to textit{pp}-waves, AdS waves, and Kundt spaces, for which both the Maxwell field and the gradient of the phase of the scalar are aligned with the null direction defining these spaces. In the Kundt family, the geometry of the two-dimensional surfaces orthogonal to the superconducting current is determined by the solutions of the two-dimensional Liouville equation, and in consequence, these surfaces are of constant curvature, as it occurs in a vacuum. The solution to the Liouville equation also acts as a potential for the Maxwell field, which we integrate into a closed-form. Using these results, we show that the combined effects of the gravitational and scalar interactions can confine the electromagnetic field within a bounded region in the surfaces transverse to the current.

Pion crystals hosting topologically stable baryons

We construct analytic (3+1)-dimensional inhomogeneous and topologically non-trivial pion systems using chiral perturbation theory. We discuss the effect of isospin asymmetry with vanishing electromagnetic interactions as well as some particular configurations with non-vanishing electromagnetic interactions. The inhomogeneous configurations of the pion fields are characterized by a non-vanishing topological charge that can be identified with baryons surrounded by a cloud of pions. This system supports a topologically protected persistent superflow. When the electromagnetic field is turned on the superflow corresponds to an electromagnetic supercurrent.

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

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.

Analytic Baby Skyrmions at Finite Density

We introduce a consistent ansatz for the baby Skyrme model in (2+1)-dimensions which is able to reduce the complete set of field equations to just one equation for the profile function in situations in which the baby baryon charge can be arbitrary. Many analytic solutions both with and without the inclusion of the effects of the minimal coupling with the Maxwell field are constructed. Linear stability and other physical properties are discussed. These analytic gauged baby Skyrmions generate a persistent $U(1)$ current which cannot be turned off continuously as it is tied to the topological charge of the baby Skyrmions themselves. In the simplest non-trivial case of a gauged baby Skyrmion, a very important role is played by the Mathieu equation with an effective coupling constant which can be computed explicitly. These configurations are a very suitable arena to test resurgence in a non-integrable context.

Analytic SU(N) Skyrmions at finite Baryon density

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.

Gravitating superconducting solitons in the (3+1)-dimensional Einstein gauged non-linear sigma-model

In this paper, we construct the first analytic examples of (3+1)-dimensional self-gravitating regular cosmic tube solutions which are superconducting, free of curvature singularities and with non-trivial topological charge in the Einstein-SU(2) non-linear sigma-model. These gravitating topological solitons at a large distance from the axis look like a (boosted) cosmic string with an angular defect given by the parameters of the theory, and near the axis, the parameters of the solutions can be chosen so that the metric is singularity free and without angular defect. The curvature is concentrated on a tube around the axis. These solutions are similar to the Cohen-Kaplan global string but regular everywhere, and the non-linear sigma-model regularizes the gravitating global string in a similar way as a non-Abelian field regularizes the Dirac monopole. Also, these solutions can be promoted to those of the fully coupled Einstein-Maxwell non-linear sigma-model in which the non-linear sigma-model is minimally coupled both to the U(1) gauge field and to General Relativity. The analysis shows that these solutions behave as superconductors as they carry a persistent current even when the U(1) field vanishes. Such persistent current cannot be continuously deformed to zero as it is tied to the topological charge of the solutions themselves. The peculiar features of the gravitational lensing of these gravitating solitons are shortly discussed.