We summarise the procedure used to find the classical masses of Higgs particle, massive gauge boson and t'Hooft-Polyakov monopole in non-Hermitian gauge field theory. Their physical regions are explored, and the mechanism of the real value of the monopole solution is analysed in different physical regions.
We have numerically calculated topological andnon-topological solitons in two spatial dimensions with Chern-Simons term. Their quantum stability, as well as that of the Maxwell vortex, is analyzed by means of bounce instantons which involve three-dimensional strings and non-topological solitons.
Static topologically-nontrivial configurations in sigma-models, for spatial dimension D \geq 2, are unstable. The question addressed here is whether such sigma-model solitons can be stabilized by steady rotation in internal space; that is, rotation in a global SO(2) symmetry. This is the mechanism which stabilizes Q-balls (non-topological solitons). The conclusion is that the Q-mechanism can stabilize topological solitons in D=2 spatial dimensions, but not for D=3.
We show that the degeneracy of topological solitons in the gauged O(3) non-linear sigma model with Chern-Simons term may be removed by chosing a self-interaction potential with symmetry - breaking minima. The topological solitons in the model has energy,charge,flux and angular momentum quantised in each topological sector.
By including potential into the flat metric, we study interaction of sine-Gordon soliton with potentials. We will show numerically that while the soliton-barrier system shows fully classical behaviour, the soliton-well system demonstrates non-classical behaviour. In particular, solitons with low velocities are trapped in the well and emit energy radiation.
We provide a proof of a formula conjectured in \cite{OU93} for some coefficients relevant in the principal vertex operator construction of a simply-laced affine algebra $\gh$. These coefficients are important for the study of the topological charges of the solitons of affine Toda theories, and the construction of representations of non-simply-laced $\gh$ and their associated Toda solitons.
We present a topological Lagrangian field theory that is geometrically similar to the Yang-Mills(-Higgs) Lagrangian, and study the Bogomol'nyi solitons contained within this theory. The topological field theory may provide an example of a dual field theory to Yang-Mills(-Higgs). The existence of a dual field theory to Yang-Mills(-Higgs) was conjectured by Montonen and Olive.
We show that when a Chern-Simons term is added to the action of $SU(N)$ ($N\geq 3$) Yang-Mills theory in 5 dimensions the usual self-dual topological solitons present in the theory necessarily pick up a (topological) electric charge.
The $O(3)$ nonlinear sigma model with its $U(1)$ subgroup gauged, where the gauge field dynamics is solely governed by a Chern-Simons term, admits both topological as well as nontopological self-dual soliton solutions for a specific choice of the potential. It turns out that the topological solitons are infinitely degenerate in any given sector.
The topological charges of the \an affine Toda solitons are considered. A general formula is presented for the number of charges associated with each soliton, as well as an expression for the charges themselves. For each soliton the charges are found to lie in the corresponding fundamental representation, though in general these representations are not filled. Each soliton's topological charges are invariant under cyclic permutations of the simple roots plus the extended root or equivalently, under the action of the Coxeter element (with a particular ordering). Multisolitons are considered and…
Two topological issues on membranes in M-theory are studied: (1) Soliton is an important subject in M-theory. Under the framework of obstruction theory with the help from framed links in $S^3$, we give a complete enumeration of topological membrane solitons in a string-admissible target-space of the form a product of Minkowskian space-times, tori, and K3-surfaces. Patching of these solitons and their topological charges are also defined and discussed. (2) Loop order of membrane scatterings is the basis for a perturbative M-theory. We explore this concept with emphases on its distinct features …
In this talk, we give new insight into one of the best-known nonlinear field theories, the Skyrme model. We present some exact relevant solutions coming from different new versions (gauged BPS baby as well as vector BPS Skyrme models) giving rise to topological solitons, and highlighting the BPS character of the theory.
An improved model for the soliton-potential interaction is presented. This model is constructed with a better approximation for adding the potential to the lagrangian through a space-time metric. The results of the model are compared with other models and the differences are discussed.
The noncommutative soliton is characterized by the use of the projection operators in non-commutative space. By using the close relation with the K-theory of $C^*$-algebra, we consider the variations of projection operators along the commutative directions and identify their topological charges. When applied to the string theory, it gives the modification of the brane charges due to tachyon background.
We study non-Abelian solitons of the Bogomol'nyi type in N=2 (d=2+1) supersymmetric Chern-Simons (CS) and Yang-Mills (YM) theory with a generic gauge group. In CS theory, we find topological, non-topological and semi-local (non-)topological vortices of non-Abelian kinds in unbroken, broken and partially broken vacua. We calculate the number of zero-modes using an index theorem and then we apply the moduli matrix formalism to realize the moduli parameters. For the topological solitons we exhaust all the moduli while we study several examples of the non-topological and semi-local solitons. We fi…
Schrödinger field theory with an attractive self-interaction possess non-topological extended solutions with a finite energy in both finite and infinite-volume cases, namely, bright solitons. The analytical form of the solution itself is well-known, though analytical investigation of the quantum fluctuations in this background still requires more thorough investigation, for instance, analytical computation of quantum corrections to this background within the saddle-point approximation. In the present work this gap is filled. Both 2-point Green's function and quantum corrections to the backgrou…
We consider a class of $N=2$ supersymmetric non--unitary theories in two--dimensional Minkowski spacetime which admit classical solitonic solutions. We show how these models can be twisted into a topological sector whose energy--momentum tensor is a BRST commutator. There is an infinite number of degrees of freedom associated to the zero modes of the solitons. As explicit realizations of such models we discuss the BRST quantization of a system of free fields, while in the interacting case we study $N=2$ complexified twisted Toda theories.
We generalize our results${}^1$ on charged topological solitons (CTS) in $4+1$ dimensional $SU(3)$ Yang-Mills-Chern-Simons (YMCS) theory to $SU(N)$. The $SU(N)$ multiplet structure of two classes of solitons associated with the maximal embeddings $SU(2)\times U(1)^{N-2}\subset SU(N)$ and $SO(3)\times U(1)^{N-3}\subset SU(N)$ and the vital role of the $SU(N)$ multiplet of topological currents is clarified. In the case of the first embedding one obtains a $^{N}C_{2}-$plet of CTS. In the second, for $N = 3$, one obtains neutral solitons which, though (classically) spinless, have magnetic moments.…
We investigate a model for a real scalar field in bidimensional space-time, described in terms of a positive semi-definite potential that presents no vacuum state. The system presents topological solutions of the BPS type, with energy density that follows a Lorentzian law. These BPS solutions differ from the standard $\tanh$-type kink, but they also support bosonic and fermionic zero modes.
In a series of recent works Ishihara and Ogawa have investigated non-topological solitons (Q-balls) in a spontaneously broken Abelian gauge theory coupled to two complex scalar fields. The present paper extends their investigations to the most general U(1)$\times$U(1) symmetric quartic potential. Also a new class of charged Q-ball solutions with vanishing self-interaction terms is investigated and some of their remarkable properties is exhibited.
Two new families of T-Dual integrable models of dyonic type are constructed. They represent specific $A_n^{(1)}$ singular Non-Abelian Affine Toda models having U(1) global symmetry. Their 1-soliton spectrum contains both neutral and U(1) charged topological solitons sharing the main properties of 4-dimensional Yang-Mills-Higgs monopoles and dyons. The semiclassical quantization of these solutions as well as the exact counterterms and the coupling constant renormalization are studied.
We provide a review of non-topological solitonic solutions arising in theories with a complex scalar field and global or gauge $U(1)$-symmetry. It covers Q-balls, homogeneous charged scalar condensates, and nonlinear localized holes and bulges in a classically stable condensate. A historical overview is followed by the discussion of properties of solutions, including their stability, from different perspectives. Solitons in models with additional massive degrees of freedom are also revisited, and their relation to one-field Q-balls is showed. We also discuss theories with a gauge field giving …
A submodel of the so-called conformal affine Toda model coupled to the matter field (CATM) is defined such that its real Lagrangian has a positive-definite kinetic term for the Toda field and a usual kinetic term for the (Dirac) spinor field. After spontaneously broken the conformal symmetry by means of BRST analysis, we end up with an effective theory, the off-critical affine Toda model coupled to the matter (ATM). It is shown that the ATM model inherits the remarkable properties of the general CATM model such as the soliton solutions, the particle/soliton correspondence and the equivacence b…
We perform a systematic analysis of the conditions under which \textit{generalized} gauge field theories of compact semisimple Lie groups exhibit electrostatic spherically symmetric non-topological soliton solutions in three space dimensions. By the term \textit{generalized}, we mean that the dynamics of the concerned fields is governed by lagrangian densities which are general functions of the quadratic field invariants, leading to physically consistent models. The analysis defines exhaustively the class of this kind of lagrangian models supporting those soliton solutions and leads to methods…
The scattering of Dirac fermions in the background fields of topological solitons of the $(2+1)$-dimensional nonlinear $O(3)$ $σ$-model is studied using both analytical and numerical methods. General formulae describing fermion scattering are obtained and the symmetry properties of the partial scattering amplitudes and elements of the $S$-matrix are determined. Within the framework of the Born approximation, the scattering amplitudes, differential cross-sections, and total cross-sections of fermion-soliton scattering are obtained in analytical forms, and their symmetry properties and asymptoti…
We study finite energy static solutions to a global symmetry breaking model in 3+1 dimensions described by an isovector scalar field. The basic features of two different types of configurations are discussed, one of them corresponding to axially symmetric multisolitons with topological charge $n$, and the other one to unstable soliton-antisoliton pairs with zero topological charge.
We present results of our studies of various scattering properties of topological solitons on obstructions in the form of holes and barriers in 1+1 dimensions. Our results are based on two models involving a ϕ^4 potential. The obstructions are characterised by a potential parameter, λwhich has a non-zero value in a certain region of space and zero elsewhere. In the first model the potential parameter is included in the potential and in the second model the potential parameter is included in the metric. Our results are based on numerical simulations and analytical considerations.
We clarify relations among topological solitons in various dimensions: a domain wall, non-Abelian vortex, magnetic monopole and Yang-Mills instanton, together with a (non-Abelian) sine-Gordon soliton, baby Skyrmion (lump) and Skyrmion. We construct a composite configuration consisting of a domain wall, vortex, magnetic monopole and Yang-Mills instanton (wall-vortex-monopole-instanton) using the effective theory technique or moduli approximation. Removing some solitons from such a composite, we obtain all possible composite solitons in the form of solitons within a soliton, including all the pr…
Topological excitations in Chern-Simons gauge theories which describe double-layer fractional quantum Hall effct are studied. There are two types of solitons; one is vortex and the other is nontrivial pseudospin textures which are so-called skyrmion or meron. Effective field theory which describes these solitons is derived by duality transformation.
We analyze topological solitons in the noncommutative plane by taking a concrete instance of the quantum Hall system with the SU(N) symmetry, where a soliton is identified with a skyrmion. It is shown that a topological soliton induces an excitation of the electron number density from the ground-state value around it. When a judicious choice of the topological charge density $J_{0}(\mathbf{x})$ is made, it acquires a physical reality as the electron density excitation $Δρ^{\text{cl}}(\mathbf{x})$ around a topological soliton, $Δρ^{\text{cl}}(\mathbf{x})=-J_{0}(% \mathbf{x})$. Hence a noncommut…
We provide complete and self-contained formulas about localization of massless/massive Abelian gauge fields on topological solitons in generic $D$ dimensions via a field dependent gauge kinetic term. The localization takes place when a stabilizer (a scalar field) is condensed in the topological soliton. We show that the localized gauge bosons are massless when the stabilizer is neutral. On the other hand, they become massive for the charged stabilizer as a consequence of interplay between the localization mechanism and the Higgs mechanism. For concreteness, we give two examples in six dimensio…
We show that three-band superconductors with broken time reversal symmetry allow magnetic flux-carrying stable topological solitons which have only a slightly higher energy than ordinary vortices. Therefore they can be induced by fluctuations or quenching the system through a phase transition. It can provide an experimental signature of the time reversal symmetry breakdown.
We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology $H^2$ of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force.
Magnetic monopoles and Q-balls are examples of topological and nontopological solitons, respectively. A new soliton state with both topological and nontopological charges is shown to also exist, given a monopole sector with a portal coupling to an additional scalar field $S$ with a global $U(1)$ symmetry. This new state, the Q-monopole-ball, is more stable than an isolated Q-ball made of only $S$ particles, and it could be stable against fissioning into monopoles and free $S$ particles. Stable Q-monopole-balls can contain large magnetic charges, providing a novel nongravitational mechanism for…
The chiral soliton lattice is an array of topological solitons realized as ground states of QCD at finite density under strong magnetic fields or rapid rotation, and chiral magnets with an easy-plane anisotropy. In such cases, topological solitons have negative energy due to topological terms originating from the chiral magnetic or vortical effect and the Dzyaloshinskii-Moriya interaction, respectively. We study quantum nucleation of topological solitons in the vacuum through quantum tunneling in $2+1$ and $3+1$ dimensions, by using a complex $ϕ^4$ (or the axion) model with a topological term …
The paper, classically, presents a special stable non-topological solitary wave packet solution in $3+1$ dimensions for an extended complex non-linear Klein-Gordon (CNKG) field system. The rest energy of this special solution is minimum among other (close) solutions i.e. it is a soliton solution. The equation of motion and other properties for this special stable solution are reduced to the same original known CNKG system.
We discover a new class of topological solitons. These solitons can exist in a space of infinite volume like, e.g., $\mathbb{R}^n$, but they cannot be placed in any finite volume, because the resulting formal solutions have infinite energy. These objects are, therefore, interpreted as totally incompressible solitons. As a first, particular example we consider (1+1) dimensional kinks in theories with a nonstandard kinetic term or, equivalently, in models with the so-called runaway (or vacummless) potentials. But incompressible solitons exist also in higher dimensions. As specific examples in (3…
The non-topological FL model is studied at finite temperature and density. The soliton solutions of the FL model in deconfinement phase transition are solved and thoroughly discussed for different boundary conditions. We indicate that the solitons before and after the deconfinement have different physical meanings: the soliton before deconfinement represents hadron, while the soliton after the deconfinement represents the bound state of quarks which leads to a sQGP phase. The corresponding phase diagram is given.
We point out that the celebrated Hawking effect of quantum instability of black holes seems to be related to a nonperturbative effect in string theory. Studying quantum dynamics of strings in the gravitational background of black holes we find classical instability due to emission of massless string excitations. The topology of a black hole seems to play a fundamental role in developing the string theory classical instability due to the effect of sigma model instantons. We argue that string theory allows for a qualitative description of black holes with very small masses and it predicts topolo…
We consider a scalar field model with a self-interaction potential that possesses a discrete vacuum manifold. We point out that this model allows for both topological as well as non-topological solitons. In (1+1) dimensions both type of solutions have finite energy, while in (3+1) dimensions, the topological solitons have finite energy per unit area only and correspond to domain walls. Non-topological solitons with finite energy do exist in (3+1) dimensions due to a non-trivial phase of the scalar field and an associated U(1) symmetry of the model, though. We construct these so-called Q-ball s…
We consider extended chiral group $Eχ$ of gauge plus chiral transformations of the quark path integral in the background gauge and present novel type of color solitons described by the effective action resulting from bosonization. O(3) solitons are formed by a chiral field including parameters with diquark quantum numbers within symplectic subgroup of $Eχ$, as well as within complete $Eχ$; isolated solitons (i.e. solitons in gluonic vacuum) can be stable due to proper asymptotics induced by background vacuum, their topological charge starts from $\pm \frac 43$ and does not coincide with the ba…
We present two- and three-dimensional simulations of the growth of quantum fluctuations of the scalar fields in supersymmetric hybrid inflation models. For a natural range of couplings, sub-horizon quantum fluctuations undergo rapid growth due to scalar field dynamics, resulting in the formation of quasi-stable non-topological solitons (inflaton condensate lumps) which dominate the post-inflation era.
We formulate a quantum coherent state picture for topological and non-topological solitons. We recognize that the topological charge arises from the infinite occupation number of zero momentum quanta flowing in one direction. Thus, the Noether charge of microscopic constituents gives rise to a topological charge in the macroscopic description. This fact explains the conservation of topological charge from the basic properties of coherent states. It also shows that no such conservation exists for non-topological solitons, which have finite mean occupation number. Consequently, they can have an …
In this paper the conditions, under which non-topological solitons are absent in the Yang-Mills theory coupled to a non-linear scalar field in Minkowski space, are obtained in a very simple way. It is also shown that non-topological solitons are absent in the theory describing the massive complex vector field coupled to the electromagnetic field in Minkowski space.
We examine some general properties of a certain class of scalar filed theory models containing non-topological soliton solutions in the context of brane world models with compact large extra dimensions. If a scalar field is allowed to propagate in extra space, then, beside standard Kaluza-Klein type excitations, a whole new class of very massive soliton-type states can exist. Depending on their abundance, they can be important dark matter candidates or give significant contribution to entropy and energy density in our universe. .
We present several new space-periodic solutions of the static vacuum Einstein equations in higher dimensions, both with and without black holes, having Kasner asymptotics. These latter solutions are referred to as gravitational solitons. Further partially compactified solutions are also obtained by taking appropriate quotients, and the topologies are computed explicitly in terms of connected sums of products of spheres. In addition, it is shown that there is a correspondence, via Wick rotation, between the spacelike slices of the solitons and black hole solutions in one dimension less. As a co…
We study the scattering properties of topological solitons on obstructions in the form of holes and barriers. We use the 'new baby Skyrme' model in (2+1) dimensions and we model the obstructions by making the coefficient of the baby skyrme model potential - position dependent. We find that that the barrier leads to the repulsion of the solitons (for low velocities) or their complete transmission (at higher velocities) with the process being essentially elastic. The hole case is different; for small velocities the solitons are trapped while at higher velocities they are transmitted with a loss …
We study the existence of smooth topological solitons and black strings as locally-stable saddles of the Euclidean gravitational action of five dimensional Einstein-Maxwell theory. These objects live in the Kaluza-Klein background of four dimensional Minkowski with an $S^1$. We compute the off-shell gravitational action in the canonical ensemble with fixed boundary data corresponding to the asymptotic radius of $S^1$, and to the electric and magnetic charges that label the solitons and black strings. We show that these objects are locally-stable in large sectors of the phase space with varying…
We propose that protein loops can be interpreted as topological domain-wall solitons. They interpolate between ground states that are the secondary structures like alpha-helices and beta-strands. Entire proteins can then be folded simply by assembling the solitons together, one after another. We present a simple theoretical model that realizes our proposal and apply it to a number of biologically active proteins including 1VII, 2RB8, 3EBX (Protein Data Bank codes). In all the examples that we have considered we are able to construct solitons that reproduce secondary structural motifs such as a…
The Casimir energy for the classically stable configurations of the topological solitons in 2D quantum antiferromagnets is studied by performing the path-integral over quantum fluctuations. The magnon fluctuation around the solitons saturating the Bogomol'nyi inequality may be viewed as a charged scalar field coupled with an effective magnetic field induced by the solitons. The magnon-soliton couping is closely related to the Pauli Hamiltonian, with which the effective action is calculated by adapting the worldline formulation of the derivative expansion for the 2+1d quantum electrodynamics in…
