<p>In this paper, we construct an exact solution of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math> Einstein-Skyrme model in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo>=</mo><mn>4</mn></math> space-time dimensions describing a charged and rotating black hole with toroidal horizon. Rotation is added by applying an improper coordinate transformation to the known static toroidal black hole with Skyrme hair, while the electric charge is supplemented by considering a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> gauge field interacting with Einstein gravity. We perform the thermal analysis in the grand canonical ensemble, explicitly showing the role that the flavor number plays. Some discussions about stability are also considered.</p>

Chile

Carla Henríquez-Baez

Marcela Lagos

Evelyn Rodríguez

Aldo Vera

Exact charged and rotating toroidal black hole in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> Einstein-Skyrme model

We derive a novel BPS bound from chiral perturbation theory minimally coupled to electrodynamics at finite isospin chemical potential. At a critical value of the isospin chemical potential, a system of three first-order differential field equations (which implies the second-order field equations) for the gauge field and the hadronic profile can be derived from the requirement to saturate the bound. These BPS configurations represent magnetic multi-vortices with quantized flux supported by a superconducting current. The corresponding topological charge density is related to the magnetic flux density, but is screened by the hadronic profile. Such a screening effect allows to derive the maximal value of the magnetic field generated by these BPS magnetic vortices, being B max = 2, 04 × 1014 G. The solution for a single BPS vortex is discussed in detail, and some physical consequences, together with the comparison with the magnetic vortices in the Ginzburg-Landau theory at critical coupling, are described.

Fabrizio Canfora

Superconducting multi-vortices and a novel BPS bound in chiral perturbation theory

We construct topological soliton solutions describing baryonic tubes and layers with modulation in the <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> non-linear sigma model coupled with ω-mesons in <math><mn>3</mn><mo>+</mo><mn>1</mn></math> dimensions. Using appropriate Ansäntze for the pionic matter field and the ω-mesons vector potential, the complete set of seven coupled partial differential equations can be solved analytically. These solutions represent modulated tubes and layers at finite volume with arbitrary baryon number, where the modulation of the solitons in one direction is determined by one of the three degrees of freedom of the pionic field, satisfying the equation of a two-dimensional free massless chiral scalar field. As expected, the inclusion of the ω-mesons to the non-linear sigma model allows to reduce the repulsion energy between baryons, which leads to a flattening of the tubes and layers in one direction, forming a kind of “nuclear linguine phase”. Also, we show that this construction can be carried out even when higher order terms in the large <math><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub></math> expansion are included -in particular the Skyrme term- without spoiling the integrability of the field equations.

Gonzalo Barriga

Italy

Matías Torres

Exact modulated hadronic tubes and layers at finite volume in a cloud of And Mesons

By incorporating two gauge connections, transgression forms provide a generalization of Chern-Simons actions that are genuinely gauge-invariant on bounded manifolds. In this work, we show that, when defined on a manifold with a boundary, the Hamiltonian formulation of a transgression field theory can be consistently carried out without the need to implement regularizing boundary terms at the level of first-class constraints. By considering boundary variations of the relevant functionals in the Poisson brackets, the surface integral in the very definition of a transgression action can be translated into boundary contributions in the generators of gauge transformations and diffeomorphisms. This prescription systematically leads to the corresponding surface charges of the theory, reducing to the general expression for conserved charges in (higher-dimensional) Chern-Simons theories when one of the gauge connections in the transgression form is set to zero.

Czechia

Pablo Pais

Poland

Patricio Salgado-Rebolledo

A note on the Hamiltonian structure of transgression forms

A remarkable exact mapping, valid for low-enough energy scales and close to a sharp boundary distribution of hadronic matter, from the (<math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional Skyrme model to the sine-Gordon theory in (<math><mn>1</mn><mo>+</mo><mn>1</mn></math>) dimensions in the attractive regime is explicitly constructed. Besides the intrinsic theoretical interest to be able to describe the prototype of nonintegrable theories (namely, quantum chromodynamics in the infrared regime) in terms of the prototype of integrable relativistic field theories (namely, sine-Gordon theory in (<math><mn>1</mn><mo>+</mo><mn>1</mn></math>) dimensions), we will show that this mapping can be extremely useful to analyze both equilibrium and out-of-equilibrium features of baryonic distributions in a cavity.

Exact mapping from the <math><mrow><mo>(</mo><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></math>-dimensional Skyrme model to the <math><mrow><mo>(</mo><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></math>-dimensional sine-Gordon theory and some applications

In this paper, using the maximal embedding of <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> into <math><mi>S</mi><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> in the Euler angles parametrization, we construct a novel family of exact solutions of the Einstein <math><mi>S</mi><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math>-Skyrme model. First, we present a hairy toroidal black hole in <math><mi>D</mi><mo>=</mo><mn>4</mn></math> dimensions. This solution is asymptotically locally anti–de Sitter and is characterized by discrete hair parameters. Then, we perform a dimensional extension of the black hole to obtain black <math><mi>p</mi></math>-branes as solutions of the Einstein <math><mi>S</mi><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math>-nonlinear sigma model in <math><mi>D</mi><mo>≥</mo><mn>5</mn></math> dimensions. These are homogeneous and topologically protected. Finally we show that, through a Wick rotation of the toroidal black hole, one can construct an exact self-gravitating instanton. The role that the flavor number <math><mi>N</mi></math> plays in the geometry and thermodynamics of these configurations is also discussed.

Patrick Concha

Exact flavored black <math><mi>p</mi></math>-branes and self-gravitating instantons from toroidal black holes with Skyrme hair

We present an exact time-dependent solution for a charged scalar field on a two-dimensional cylinder, that can be interpreted as representing a long-standing excitation on a <math><mi>S</mi></math>-wave superconducting state, which propagates along a nanotube constructed out of twisted bilayer graphene. The solution has a topological charge characterized by an integer number, which counts the winding of the Higgs phase winds around the cylinder. The resulting electric current generates its own electromagnetic field in a self-consistent way, without the need of any external fields to keep it alive.

Alex Giacomini

Argentina

Nicolás Grandi

Julio Oliva

Solitonic self-sustained charge and energy transport on the superconducting cylinder

In this manuscript, we discuss a remarkable phenomenon concerning nonlinear and nonintegrable field theories in (<math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>) dimensions, living at finite density and possessing nontrivial topological charges and non-Abelian internal symmetries (both local and global). With suitable types of Ansätze, one can construct infinite-dimensional families of analytic solutions with nonvanishing topological charges (representing the baryonic number) labeled by both two integer numbers and by free scalar fields in (<math><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>) dimensions. These exact configurations represent (<math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional topological solitons hosting (<math><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional chiral modes localized at the energy density peaks. First, we analyze the Yang-Mills-Higgs model, in which the fields depend on all the space-time coordinates (to keep alive the topological Chern-Simons charge), but in such a way to reduce the equations system to the field equations of two-dimensional free massless chiral scalar fields. Then, we move to the nonlinear sigma model, showing that a suitable Ansatz reduces the field equations to the one of a two-dimensional free massless scalar field. Then, we discuss the Skyrme model concluding that the inclusion of the Skyrme term gives rise to a chiral two-dimensional free massless scalar field (instead of a free massless field in two dimensions as in the nonlinear sigma model) describing analytically spatially modulated hadronic layers and tubes. The comparison of the present approach both with the instanton-dyon liquid approach and with lattice QCD is shortly outlined.

Diego Hidalgo

Enzo Meneses

Infinite conformal symmetry and emergent chiral fields of topologically nontrivial configurations: From Yang-Mills-Higgs theory to the Skyrme model

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.

On the robustness of solitons crystals in the Skyrme model

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.