We construct analytic ( 3 + 1 )-dimensional inhomogeneous and topologically nontrivial pion systems using chiral perturbation theory. We discuss the effect of isospin asymmetry with vanishing ...electromagnetic interactions as well as some particular configurations with nonvanishing electromagnetic interactions. The inhomogeneous configurations of the pion fields are characterized by a nonvanishing 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.
The first analytic solutions representing baryonic layers living at finite baryon density within a constant magnetic field in the gauged Skyrme model are constructed. A remarkable feature of these ...configurations is that, if the Skyrme term is neglected, then these baryonic layers in the constant magnetic background cannot be found analytically and their energies grow very fast with the magnetic field. On the other hand, if the Skyrme term is taken into account, the field equations can be solved analytically and the corresponding solutions have a smooth limit for large magnetic fields. Thus, the Skyrme term discloses the universal character of these configurations living at finite Baryon density in a constant magnetic field. The classical gran-canonical partition function of these configurations can be expressed explicitly in terms of the Pearcey integral. This fact allows us to determine analytically the Stokes lines of the partition function and the corresponding dependence on the baryonic chemical potential as well as on the external magnetic field. In this way, we can determine various critical curves in the (μB−Bext) plane which separates different physical behaviors. These families of inhomogeneous baryonic condensates can be also dressed with chiral conformal excitations of the solutions representing modulations of the layers themselves. Some physical consequences are analyzed.
A
bstract
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 allow to compare explicitly the physical properties of nuclear spaghetti and lasagna phases. Our construction shows explicitly that, at lower densities, configurations with
N
= 2 light flavors are favored while, at higher densities, configurations with
N
= 3 are favored. Our construction also proves that in the high density regime (but still well within the range of validity of the Skyrme model) the lasagna configurations are favored while at low density the spaghetti configurations are favored. Moreover, the integrability property of the present configurations is not spoiled by the inclusion of the subleading corrections to the Skyrme model arising in the ’t Hooft expansion. Finally, we briefly discuss the large
N
limit of our configurations.
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
σ
-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
σ
-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
σ
-model in which the non-linear
σ
-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.
Analytic baby skyrmions at finite density Barsanti, Marco; Bolognesi, Stefano; Canfora, Fabrizio ...
European physical journal. C, Particles and fields,
12/2020, Volume:
80, Issue:
12
Journal Article
Peer reviewed
Open access
We study the baby Skyrme model in (2+1)-dimensions built on a finite cylinder. To this end, we introduce a consistent ansatz which is able to reduce the complete set of field equations to just one ...equation for the profile function for arbitrary baryon charge. Many analytic solutions both with and without the inclusion of the effects of the minimal coupling with the Maxwell field are constructed. The baby skyrmions appear as a sequence of rings along the cylinder, leading to a periodic shape in the baryon density. 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.
A
bstract
We employ path integral methods to calculate the Casimir energy and force densities in a chiral extension of QED. Manifestly gauge invariant perfect electromagnetic boundary conditions, a ...natural generalization of perfect electric and perfect magnetic conditions, are implemented directly in the action by the usage of auxiliary fields. The chiral properties of the vacuum are modelled using a background
θ
field, and we introduce techniques to efficiently calculate the path integral in this chiral medium. The flexibility of our method allows us to naturally obtain results for a variety of configurations, and where comparison is possible our results are in perfect agreement with existing literature. Among these are multiple situations where a repulsive Casimir force is possible.
An exact hairy asymptotically locally AdS black hole solution with a flat horizon in the Einstein-nonlinear sigma model system in (3+1) dimensions is constructed. The ansatz for the nonlinear SU(2) ...field is regular everywhere and depends explicitly on Killing coordinates, but in such a way that its energy–momentum tensor is compatible with a metric with Killing fields. The solution is characterized by a discrete parameter which has neither topological nor Noether charge associated with it and therefore represents a hair. A U(1) gauge field interacting with Einstein gravity can also be included. The thermodynamics is analyzed. Interestingly, the hairy black hole is always thermodynamically favoured with respect to the corresponding black hole with vanishing Pionic field.
In this work we analize how the inclusion of extra mesonic degrees of freedom affect the finite density solitons crystals of the Skyrme model. In particular, the first analytic examples of hadronic ...crystals at finite baryon density in both the Skyrme ω-mesons model as well as for the Skyrme ρ-mesons theory are constructed. These configurations have arbitrary topological charge and describe crystals of baryonic tubes surrounded by a cloud of vector-mesons. In the ω-mesons case, it is possible to reduce consistently the complete set of seven coupled non-linear field equations to just two integrable differential equations; one ODE for the Skyrmion profile and one PDE for the ω-mesons field. This analytical construction allows to show explicitly how the inclusion of ω-mesons in the Skyrme model reduces the repulsive interaction energy between baryons. In the Skyrme ρ-mesons case, it is possible to construct analytical solutions using a meron-type ansatz and fixing one of the couplings of the ρ-mesons action in terms of the others. We show that, quite remarkably, the values obtained for the coupling constants by requiring the consistency of our ansatz are very close to the values used in the literature to reduce nuclei binding energies of the Skyrme model without vector-mesons. Moreover, our analytical results are in qualitative agreement with the available results on the nuclear spaghetti phase.
The Gribov problem in the presence of a background field is analyzed: in particular, we study the Gribov copies equation in the Landau–De Witt gauge as well as the semi-classical Gribov gap equation. ...As background field, we choose the simplest non-trivial one which corresponds to a constant gauge potential with non-vanishing component along the Euclidean time direction. This kind of constant non-Abelian background fields is very relevant in relation with (the computation of) the Polyakov loop but it also appears when one considers the non-Abelian Schwinger effect. We show that the Gribov copies equation is affected directly by the presence of the background field, constructing an explicit example. The analysis of the Gribov gap equation shows that the larger the background field, the smaller the Gribov mass parameter. These results strongly suggest that the relevance of the Gribov copies (from the path integral point of view) decreases as the size of the background field increases.
A
bstract
We construct an analytic black hole solution in SU(2) Einstein-Yang-Mills theory in five dimensions supporting a Meron field. The gauge field is proportional to a pure gauge and has a ...non-trivial topological charge. The would-be singularity at the Meron core gets shielded from the exterior by the black hole horizon. The metric has only one integration constant, namely, its ADM mass, which is shown to be finite once an appropriate boundary term is added to the action. The thermodynamics is also worked out, and a first-order phase transition, similar to the one occurring in the Reissner-Nordström case is identified. We also show that the solution produces a
spin from isospin effect
, i.e., even though the theory is constructed out of bosons only, the combined system of a scalar field and this background may become fermionic. More specifically, we study scalar excitations in this purely bosonic background and find that the system describes fermionic degrees of freedom at spatial infinity. Finally, for the asymptotically
AdS
5
case, we study its consequences in the context of the AdS/CFT correspondence.
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