arXiv subjects

J. Sanchez-Guillen

Publications and source records attributed to J. Sanchez-Guillen.

At least 55 records · Page 3Linked to original sources

arXiv2009

Compact shell solitons in K field theories

Some models providing shell-shaped static solutions with compact support (compactons) in 3+1 and 4+1 dimensions are introduced, and the corresponding exact solutions are calculated analytically. These solutions turn out to be topological solitons, and may be classified as maps $S^3 \to S^3$ and suspended Hopf maps, respectively. The Lagrangian of these models is given by a scalar field with a non-standard kinetic term (K field) coupled to a pure Skyrme term restricted to $S^2$, rised to the appropriate power to avoid the Derrick scaling argument. Further, the existence of infinitely many exact shell solitons is explained using the generalized integrability approach. Finally, similar models allowing for non-topological compactons of the ball type in 3+1 dimensions are briefly discussed.

hep-th↗

arXiv2009

On the objective existence of physical processes: a physicist's philosophical view

Inspired by philosophical ideas of Boltzmann, which are briefly recalled, we provide strong support for the possibility and convenience of a realistic world picture, properly nuanced. The arguments have consequences for the interpretation of quantum mechanics, and for relevant concepts of quantum field and string theory, like monopoles and branes. Our view is illustrated with a cybernetic analogy and complemented with a summary of the basic philosophical concepts.

quant-ph↗

arXiv2009

k-defects as compactons

We argue that topological compactons (solitons with compact support) may be quite common objects if $k$-fields, i.e., fields with nonstandard kinetic term, are considered, by showing that even for models with well-behaved potentials the unusual kinetic part may lead to a power-like approach to the vacuum, which is a typical signal for the existence of compactons. The related approximate scaling symmetry as well as the existence of self-similar solutions are also discussed. As an example, we discuss domain walls in a potential Skyrme model with an additional quartic term, which is just the standard quadratic term to the power two. We show that in the critical case, when the quadratic term is neglected, we get the so-called quartic $ϕ^4$ model, and the corresponding topological defect becomes a compacton. Similarly, the quartic sine-Gordon compacton is also derived. Finally, we establish the existence of topological half-compactons and study their properties.

hep-th↗

arXiv2009

Integrable theories and loop spaces: fundamentals, applications and new developments

We review our proposal to generalize the standard two-dimensional flatness construction of Lax-Zakharov-Shabat to relativistic field theories in d+1 dimensions. The fundamentals from the theory of connections on loop spaces are presented and clarified. These ideas are exposed using mathematical tools familiar to physicists. We exhibit recent and new results that relate the locality of the loop space curvature to the diffeomorphism invariance of the loop space holonomy. These result are used to show that the holonomy is abelian if the holonomy is diffeomorphism invariant. These results justify in part and set the limitations of the local implementations of the approach which has been worked out in the last decade. We highlight very interesting applications like the construction and the solution of an integrable four dimensional field theory with Hopf solitons, and new integrability conditions which generalize BPS equations to systems such as Skyrme theories. Applications of these ideas leading to new constructions are implemented in theories that admit volume preserving diffeomorphisms of the target space as symmetries. Applications to physically relevant systems like Yang Mills theories are summarized. We also discuss other possibilities that have not yet been explored.

hep-th↗

arXiv2008

Compact gauge K vortices

We investigate a version of the abelian Higgs model with a non-standard kinetic term (K field theory) in 2+1 dimensions. The existence of vortex type solutions with compact support (topological compactons) is established by a combination of analytical and numerical methods. This result demonstrates that the concept of compact solitons in K field theories can be extended to higher dimensions.

hep-th↗

arXiv2008

Pullback of the Volume Form, Integrable Models in Higher Dimensions and Exotic Textures

A procedure allowing for the construction of Lorentz invariant integrable models living in d+1 dimensional space-time and with an n dimensional target space is provided. Here, integrability is understood as the existence of the generalized zero-curvature formulation and infinitely many conserved quantities. A close relation between the Lagrange density of the integrable models and the pullback of the pertinent volume form on target space is established. Moreover, we show that the conserved currents are Noether currents generated by the volume preserving diffeomorphisms. Further, we show how such models may emerge via abelian projection of some gauge theories. Then we apply this framework to the construction of integrable models with exotic textures. Particularly, we consider integrable models providing exact suspended Hopf maps i.e., solitons with a nontrivial topological charge of pi_4(S^3). Finally, some families of integrable models with solitons of pi_n(S^n) type are constructed. Infinitely many exact solutions with arbitrary value of the topological index are found. In addition, we demonstrate that they saturate a Bogomolny bound.

hep-th↗

arXiv2008

Infinitely many conservation laws in self-dual Yang--Mills theory

Using a nonlocal field transformation for the gauge field known as Cho--Faddeev--Niemi--Shabanov decomposition as well as ideas taken from generalized integrability, we derive a new family of infinitely many conserved currents in the self-dual sector of SU(2) Yang-Mills theory. These currents may be related to the area preserving diffeomorphisms on the reduced target space. The calculations are performed in a completely covariant manner and, therefore, can be applied to the self-dual equations in any space-time dimension with arbitrary signature.

hep-th↗

arXiv2008

K fields, compactons, and thick branes

K fields, that is, fields with a non-standard kinetic term, allow for soliton solutions with compact support, i.e., compactons. Compactons in 1+1 dimensions may give rise to topological defects of the domain wall type and with finite thickness in higher dimensions. Here we demonstrate that, for an appropriately chosen kinetic term, propagation of linear perturbations is completely suppressed outside the topological defect, confining the propagation of particles inside the domain wall. On the other hand, inside the topological defect the propagation of linear perturbations is of the standard type, in spite of the non-standard kinetic term. Consequently, this compacton domain wall may act like a brane of finite thickness which is embedded in a higher dimensional space, but to which matter fields are constrained. In addition, we find strong indications that, when gravity is taken into account, location of gravity in the sense of Randall--Sundrum works for these compacton domain walls. When seen from the bulk, these finite thickness branes, in fact, cannot be distinguished from infinitely thin branes.

hep-th↗

arXiv2008

Conservation laws in Skyrme-type models

The zero curvature representation of Zakharov and Shabat has been generalized recently to higher dimensions and has been used to construct non-linear field theories which either are integrable or contain integrable submodels. The Skyrme model, for instance, contains an integrable subsector with infinitely many conserved currents, and the simplest Skyrmion with baryon number one belongs to this subsector. Here we use a related method, based on the geometry of target space, to construct a whole class of theories which are either integrable or contain integrable subsectors (where integrability means the existence of infinitely many conservation laws). These models have three-dimensional target space, like the Skyrme model, and their infinitely many conserved currents turn out to be Noether currents of the volume-preserving diffeomorphisms on target space. Specifically for the Skyrme model, we find both a weak and a strong integrability condition, where the conserved currents form a subset of the algebra of volume-preserving diffeomorphisms in both cases, but this subset is a subalgebra only for the weak integrable submodel.

hep-th↗

arXiv2008

Integrable subsystem of Yang--Mills dilaton theory

With the help of the Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field, we find an integrable subsystem of SU(2) Yang-Mills theory coupled to the dilaton. Here integrability means the existence of infinitely many symmetries and infinitely many conserved currents. Further, we construct infinitely many static solutions of this integrable subsystem. These solutions can be identified with certain limiting solutions of the full system, which have been found previously in the context of numerical investigations of the Yang-Mills dilaton theory. In addition, we derive a Bogomolny bound for the integrable subsystem and show that our static solutions are, in fact, Bogomolny solutions. This explains the linear growth of their energies with the topological charge, which has been observed previously. Finally, we discuss some generalisations.

hep-th↗

arXiv2007

A first integration of some knot soliton models

Recently it has been shown that there exists a sector within the Faddeev-Niemi model for which the equations of motion may be reduced to first order equations. However, no solutions to that sector have been given. It is not even known whether this sector contains topologically nontrivial solutions, at all. Here, we show that two models with analytically known Hopf solitons, namely the Nicole and the Aratyn-Ferreira-Zimerman models, possess sectors which can be integrated to first order partial differential equations. The main result is that these sectors are topologically nontrivial. In fact, all analytically known hopfions belong to them.

hep-th↗

arXiv2007

Comment on ``Reduction of static field equation of Faddeev model to first order PDE'', arXiv:0707.2207

The authors of the article Phys. Lett. B 652 (2007) 384, (arXiv:0707.2207), propose an interesting method to solve the Faddeev model by reducing it to a set of first order PDEs. They first construct a vectorial quantity $\bm α$, depending on the original field and its first derivatives, in terms of which the field equations reduce to a linear first order equation. Then they find vectors $\bm α_1$ and $\bm α_2$ which identically obey this linear first order equation. The last step consists in the identification of the $\bm α_i$ with the original $\bm α$ as a function of the original field. Unfortunately, the derivation of this last step in the paper cited above contains an error which invalidates most of its results.

hep-th↗

arXiv2007

Integrability in Theories with Local U(1) Gauge Symmetry

Using a recently developed method, based on a generalization of the zero curvature representation of Zakharov and Shabat, we study the integrability structure in the Abelian Higgs model. It is shown that the model contains integrable sectors, where integrability is understood as the existence of infinitely many conserved currents. In particular, a gauge invariant description of the weak and strong integrable sectors is provided. The pertinent integrability conditions are given by a U(1) generalization of the standard strong and weak constraints for models with two dimensional target space. The Bogomolny sector is discussed, as well, and we find that each Bogomolny configuration supports infinitely many conserved currents. Finally, other models with U(1) gauge symmetry are investigated.

hep-th↗

arXiv2007

Spin in the Worldline Path Integral in 2+1 Dimensions

We construct a worldline path integral for the effective action and propagator of a Dirac field in 2+1 dimensions in an Abelian gauge field background. Integrating over an auxiliary gauge group variable we derive a worldline action depending only on $x(τ)$, the spacetime paths. We show that that action is a combination of a kinetic term plus a spin action. The first is proportional to $δ[\dot{x}^2(τ)- 1]$. The second agrees exactly with the spin action one should expect for a spin-1/2 field.

hep-th↗

arXiv2006

New Integrable Sectors in Skyrme and 4-dimensional CP^n Model

The application of a weak integrability concept to the Skyrme and $CP^n$ models in 4 dimensions is investigated. A new integrable subsystem of the Skyrme model, allowing also for non-holomorphic solutions, is derived. This procedure can be applied to the massive Skyrme model, as well. Moreover, an example of a family of chiral Lagrangians providing exact, finite energy Skyrme-like solitons with arbitrary value of the topological charge, is given. In the case of $CP^n$ models a tower of integrable subsystems is obtained. In particular, in (2+1) dimensions a one-to-one correspondence between the standard integrable submodel and the BPS sector is proved. Additionally, it is shown that weak integrable submodels allow also for non-BPS solutions. Geometric as well as algebraic interpretations of the integrability conditions are also given.

hep-th↗

arXiv2006

Soliton stability in some knot soliton models

We study the issue of stability of static soliton-like solutions in some non-linear field theories which allow for knotted field configurations. Concretely, we investigate the AFZ model, based on a Lagrangian quartic in first derivatives with infinitely many conserved currents, for which infinitely many soliton solutions are known analytically. For this model we find that sectors with different (integer) topological charge (Hopf index) are not separated by an infinite energy barrier. Further, if variations which change the topological charge are allowed, then the static solutions are not even critical points of the energy functional. We also explain why soliton solutions can exist at all, in spite of these facts. In addition, we briefly discuss the Nicole model, which is based on a sigma-model type Lagrangian. For the Nicole model we find that different topological sectors are separated by an infinite energy barrier.

hep-th↗

arXiv2006

Hopf solitons and Hopf Q-balls on S^3

Field theories with a $S^2$-valued unit vector field living on $S^3 \times \RR$ space-time are investigated. The corresponding eikonal equation, which is known to provide an integrable sector for various sigma models in different spaces, is solved giving static as well as time-dependent multiply knotted configurations on $S^3$ with arbitrary values of the Hopf index. Using these results, we then find a set of hopfions with topological charge $Q_H=m^2$, $m \in \mathbf{Z}$, in the integrable subsector of the pure $CP^1$ model. In addition, we show that the $CP^1$ model with a potential term provides time-dependent solitons. In the case of the so-called "new baby Skyrme" potential we find, e.g., exact stationary hopfions, i.e., topological $Q$-balls. Our results further enable us to construct exact static and stationary Hopf solitons in the Faddeev--Niemi model with or without the new baby Skyrme potential. Generalizations for a large class of models are also discussed.

hep-th↗

arXiv2006

Investigation of the Nicole model

We study soliton solutions of the Nicole model - a non-linear four-dimensional field theory consisting of the CP^1 Lagrangian density to the non-integer power 3/2 - using an ansatz within toroidal coordinates, which is indicated by the conformal symmetry of the static equations of motion. We calculate the soliton energies numerically and find that they grow linearly with the topological charge (Hopf index). Further we prove this behaviour to hold exactly for the ansatz. On the other hand, for the full three-dimensional system without symmetry reduction we prove a sub-linear upper bound, analogously to the case of the Faddeev-Niemi model. It follows that symmetric solitons cannot be true minimizers of the energy for sufficiently large Hopf index, again in analogy to the Faddeev-Niemi model.

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