Solitons In Field Theory Research Articles

Q-balls in the presence of attractive force

Q-balls are non-topological solitons in field theories whose stability is typically guaranteed by the existence of a global conserved charge. A classic realization is the Friedberg-Lee-Sirlin (FLS) Q-ball in a two-scalar system where a real scalar χ triggers symmetry breaking and confines a complex scalar Φ with a global U(1) symmetry. A quartic interaction κχ2|Φ|2 with κ > 0 is usually considered to produce a nontrivial Q-ball configuration, and this repulsive force contributes to its stability. On the other hand, the attractive cubic interaction Λχ|Φ|2 is generally allowed in a renormalizable theory and could induce an instability. In this paper, we study the behavior of the Q-ball under the influence of this attractive force which has been overlooked. We find approximate Q-ball solutions in the limit of weak and moderate force couplings using the thin-wall and thick-wall approximations respectively. Our analytical results are consistent with numerical simulations and predict the parameter dependencies of the maximum charge. A crucial difference with the ordinary FLS Q-ball is the existence of the maximum charge beyond which the Q-ball solution is classically unstable. Such a limitation of the charge fundamentally affects Q-ball formation in the early Universe and could plausibly lead to the formation of primordial black holes.

Mock-integrability and stable solitary vortices

Localized soliton-like solutions to a (2+1)-dimensional hydro-dynamical evolution equation are studied numerically. The equation is the so-called Williams–Yamagata–Flierl equation, which governs geostrophic fluid in a certain parameter range. Although the equation does not have an integrable structure in the ordinary sense, we find there exist shape-keeping solutions with a very long life in a special background flow and an initial condition. The stability of the localization at the fusion process of two soliton-like objects is also investigated. As for the indicator of the long-term stability of localization, we propose a concept of configurational entropy, which has been introduced in analysis for non-topological solitons in field theories.

Holography for field theory solitons

We extend a well-known D-brane construction of the AdS/dCFT correspondence to non-abelian defects. We focus on the bulk side of the correspondence and show that there exists a regime of parameters in which the low-energy description consists of two approximately decoupled sectors. The two sectors are gravity in the ambient spacetime, and a six-dimensional supersymmetric Yang-Mills theory. The Yang-Mills theory is defined on a rigid AdS4 × S2 background and admits sixteen supersymmetries. We also consider a one-parameter deformation that gives rise to a family of Yang-Mills theories on asymptotically AdS4 × S2 spacetimes, which are invariant under eight supersymmetries. With future holographic applications in mind, we analyze the vacuum structure and perturbative spectrum of the Yang-Mills theory on AdS4 × S2, as well as systems of BPS equations for finite-energy solitons. Finally, we demonstrate that the classical Yang-Mills theory has a consistent truncation on the two-sphere, resulting in maximally supersymmetric Yang-Mills on AdS4.

Relativistic Collective Coordinate System of Solitons and Spinning Skyrmion

We consider constructing the relativistic system of collective coordinates of a field theory soliton on the basis of a simple principle: The collective coordinates must be introduced into the static solution in such a way that the equation of motion of the collective coordinates ensures that of the original field theory. As an illustration, we apply this principle to the quantization of spinning motion of the Skyrmion by incorporating the leading relativistic correction to the rigid body approximation. We calculate the decay constant and various static properties of nucleons, and find that the relativistic corrections are in the range of 5% -- 20%. We also examine how the baryons deform due to the spinning motion.

Relativistic collective coordinate quantization of solitons: Spinning Skyrmion

We develop a consistent relativistic generalization of collective coordinate quantization of field theory solitons. Our principle of introducing collective coordinates is that the equations of motion of the collective coordinates ensure those of the original field theory. We illustrate this principle with the quantization of spinning degrees of freedom of Skyrmion representing baryons. We calculate the leading relativistic corrections to the static properties of nucleons, and find that the corrections are non-negligible ones of 10% to 20%.

Non-topological solitons in field theories with kinetic self-coupling

We investigate some fundamental features of a class of non-linear relativistic Lagrangian field theories with kinetic self-coupling. We focus our attention upon theories admitting static, spherically symmetric solutions in three space dimensions which are finite-energy and stable. We determine general conditions for the existence and stability of these non-topological soliton solutions. In particular, we perform a linear stability analysis that goes beyond the usual Derrick-like criteria. On the basis of these considerations we obtain a complete characterization of the soliton-supporting members of the aforementioned class of non-linear field theories. We then classify the family of soliton-supporting theories according to the central and asymptotic behaviors of the soliton field, and provide illustrative explicit examples of models belonging to each of the corresponding sub-families. In the present work we restrict most of our considerations to one and many-components scalar models. We show that in these cases the finite-energy static spherically symmetric solutions are stable against charge-preserving perturbations, provided that the vacuum energy of the model vanishes and the energy density is positive definite. We also discuss briefly the extension of the present approach to models involving other types of fields, but a detailed study of this more general scenario will be addressed in a separate publication.

Semiclassical quantization of the giant magnon

Solitons in field theory provide a window into regimes not directly accessible by the fundamental perturbative degrees of freedom. Motivated by interest in the worldsheet S-matrix of string theory in AdS5 × S5 in the limit of infinite worldsheet volume we consider the semiclassical quantization of a particular soliton of this theory: the Hofman-Maldacena `giant magnon' spinning string. We obtain explicit formulas for the complete spectrum of bosonic and fermionic fluctuations around the giant magnon. As an application of these results we confirm that the one-loop correction to the classical energy vanishes as expected.

Selfgravitating electroweak strings

We obtain selfgravitating multi-string configurations for the Einstein–Weinberg–Salam model, in terms of solutions for a nonlinear elliptic system of Liouville type whose solvability was posed as an open problem in Yang (Solitons in Field Theory and Nonlinear Analysis, Springer, New York, 2001).

Remark on intersecting solitons in 4D noncommutative scalar field theory

We examine the intersections, fluctuations and deformations of codimension two solitons in field theory on a noncommutative Euclidean ${R}^{4},$ in the limit of large noncommutativity. We find that holomorphic deformations are zero modes of flat branes, and we show that there is a zero mode localized at the intersection of two solitons.

Stability of neural networks and solitons of field theory.

The layers of a feed-forward neural network are interpreted as a cascade of field theories. The stability of the neural network is interpreted as the topological stability of kink solutions. An explicit example is shown for a three-class problem with their field theoretical Lagrangian equations.

SPIN–STATISTICS THEOREMS WITHOUT RELATIVITY OR FIELD THEORY

Conventional proofs of the spin–statistics theorem either use relativistic quantum field theory or concern field theory solitons. We here construct new proofs of this theorem for spinning particles. They are extensions of previous work on spinless particles and require neither relativity nor field theory. They do, however, assume certain continuity conditions involving the existence of antiparticles. Non-Abelian statistics, such as parastatistics and braid statistics of order 2 or more, are excluded in our framework.