We compute the one-loop quantum corrections to the kink energies of the sinh-deformed $ϕ^{4}$ and $φ^{6}$ models in one space and one time dimensions. These models are constructed from the well-known polynomial $ϕ^{4}$ and $φ^{6}$ models by a deformation procedure. We also compute the vacuum polarization energy to the non-polynomial function $U(ϕ)=\frac{1}{4}(1-\sinh^{2}ϕ)^{2}$. This potential approaches the $ϕ^{4}$ model in the limit of small values of the scalar function. These energies are extracted from scattering data for fluctuations about the kink solutions. We show that for certain topological sectors with non-equivalent vacua the kink solutions of the sinh-deformed models are destabilized.
Guided by a study of kink-antikink scattering in the Gross-Neveu model and other known solutions of the Hartree-Fock approach of a particularly simple type, we demonstrate a quantitative relationship between three different problems: Quantized 1+1-dimensional fermions in the large N limit, solitons of the classical sinh-Gordon equation and classical strings moving in 3-dimensional anti de Sitter space. Aside from throwing light on the relationship between quantum field theory and classical physics, this points to the full solvability of the dynamical N-kink-antikink problem in the Gross-Neveu …
Recently it was shown that kink baryons and kink-antikink scattering in the massless Gross-Neveu model are closely related to one- and two-soliton solutions of the sinh-Gordon equation. Here we generalize these findings to the case of n kinks and antikinks. Using the known n soliton solution of the sinh-Gordon equation, we solve the general n kink-antikink scattering problem in the large N Gross-Neveu model analytically, mapping the time-dependent Hartree-Fock approach onto inverse scattering theory.
We consider the scattering of kinks of the sinh-deformed $φ^4$ model, which is obtained from the well-known $φ^4$ model by means of the deformation procedure. Depending on the initial velocity $v_{in}$ of the colliding kinks, different collision scenarios are realized. There is a critical value $v_{cr}$ of the initial velocity, which separates the regime of reflection (at $v_{in}>v_{cr}$) and that of a complicated interaction (at $v_{in}<v_{cr}$) with kinks' capture and escape windows. Besides that, at $v_{in}$ below $v_{cr}$ we observe the formation of a bound state of two oscillons, as well …
The q-deformed kink of the $λϕ^4-$model is obtained via the normalisable ground state eigenfunction of a fluctuation operator associated with the q-deformed hyperbolic functions. From such a bosonic zero-mode the q-deformed potential in 1+1 dimensions is found, and we show that the q-deformed kink solution is a kink displaced away from the origin.
We study kink-antikink collisions in a model which interpolates smoothly between the completely integrable sine-Gordon theory, the $ϕ^4$ model, and a $ϕ^6$-like model with three degenerate vacua. We find a rich variety of behaviours, including integrability breaking, resonance windows with increasingly irregular patterns, and new types of windows near the $ϕ^6$-like regime. False vacua, extra kink modes and kink fragmentation play important roles in the explanations of these phenomena. Our numerical studies are backed up by detailed analytical considerations.
Two hyperbolic-deformed field theoretic models are discussed. In both of them, due to the effect of specific deformation function on the well known $φ^4$ and $φ^6$ models, their internal structure may change significantly. Unlike the $φ^4$ kinks solutions, which has only one internal mode in addition to its translational mode, the kinks of the hyperbolic-deformed $φ^4$ model can have several internal modes. Moreover, the deformation on the $φ^6$ model has other interesting features, because the kinks of the $φ^6$ model have only a zero mode and the deformation may cause the appearance of inter…
We continue the study of form factors of descendant operators in the sinh- and sine-Gordon models in the framework of the algebraic construction proposed in [arXiv:0812.4776]. We find the algebraic construction to be related to a particular limit of the tensor product of the deformed Virasoro algebra and a suitably chosen Heisenberg algebra. To analyze the space of local operators in the framework of the form factor formalism we introduce screening operators and construct singular and cosingular vectors in the Fock spaces related to the free field realization of the obtained algebra. We show t…
We identify the kinks of a deformed O(3) linear Sigma model as the solutions of a set of first-order systems of equations; the above model is a generalization of the MSTB model with a three-component scalar field. Taking into account certain kink energy sum rules we show that the variety of kinks has the structure of a moduli space that can be compactified in a fairly natural way. The generic kinks, however, are unstable and Morse Theory provides the framework for the analysis of kink stability.
We study some properties of kink solutions of the model with non-polynomial potential obtained by deforming the well-known $φ^6$ field model. We consider the excitation spectrum of the kink. We also discuss the properties of the `kink+antikink' system as a whole that are not inherent to a solitary kink or antikink.
A method for describing the quantum kink states in the semi-classical limit of several (1+1)-dimensional field theoretical models is developed. We use the generalized zeta function regularization method to compute the one-loop quantum correction to the masses of the kink in the sine-Gordon and cubic sinh-Gordon models and another two ${\rm P}(ϕ)_2$ systems with polynomial self-interactions.
We consider the problem of calculating the Casimir energies in the winding sectors of Fateev's SS-model, which is an integrable two-parameter deformation of the O(4) non-linear sigma model in two dimensions. This problem lies beyond the scope of all traditional methods of integrable quantum field theory including the thermodynamic Bethe ansatz and non-linear integral equations. Here we propose a solution based on a remarkable correspondence between classical and quantum integrable systems and express the winding energies in terms of certain solutions of the classical sinh-Gordon equation.
It is shown how a integrable mechanical system provides all the localized static solutions of a deformation of the linear O(N)-sigma model in two space-time dimensions. The proof is based on the Hamilton-Jacobi separability of the mechanical analogue system that follows when time-independent field configurations are being considered. In particular, we describe the properties of the different kinds of kinks in such a way that a hierarchical structure of solitary wave manifolds emerges for distinct N.
In this work we investigate the issue of gravity and fermion localization and resonances in $(4,1)$-branes constructed with one scalar field coupled with gravity in deformed models. Such models give solutions for the scalar field that is the usual kink solution in the extra dimension for a parameter $p=1$ and deformations with a two-kink profile for odd $p>1$. Gravity is localized and resonant modes are found for small values of $p$. The coupling between the scalar field and spinors is a necessary condition for fermions to be localized on such branes. After performing a chiral decomposition of…
We have studied the space-reflection symmetries of some soliton solutions of deformed sine-Gordon models in the context of the quasi-integrability concept. Considering a dual pair of anomalous Lax representations of the deformed model we compute analytically and numerically an infinite number of alternating conserved and asymptotically conserved charges through a modification of the usual techniques of integrable field theories. The charges associated to two-solitons with a definite parity under space-reflection symmetry, i.e. kink-kink (odd parity) and kink-antikink (even parity) scatterings …
We consider a class of topological defects in $(1,1)$-dimensions with a deformed $ϕ^4$ kink structure whose stability analysis leads to a Schrödinger-like equation with a zero-mode and at least one vibrational (shape) mode. We are interested in the dynamics of kink-antikink collisions, focusing on the structure of two-bounce windows. For small deformation and for one or two vibrational modes, the observed two-bounce windows are explained by the standard mechanism of a resonant effect between the first vibrational and the translational modes. With the increasing of the deformation, the effect o…
We construct models of self-interacting scalar fields whose BPS solutions exhibit kink profiles which can be continuously deformed into two-kinks by varying one of the parameters of the self-interacting potential. The effective models are obtained from other models with two interacting scalar fields. The effective models are then applied in a brane-world scenario where we analyze the consequences of the thicker branes in the warped geometry and in the localization of gravity.
Sine-Gordon deformed defects that exhibit unusual phenomenological features on the topological charge are investigated. The possibility of a smooth and continuous transition between topological (non null charge) and non-topological (null charge) scenarios of deformed defects supported by sine-Gordon structures is evinced by the analytical calculation of topological charges and localized energy distributions. By describing cyclic deformation chains, we show that a triggering sine-Gordon model simultaneously supports kink and lump-like defects, whose topological mass values are closed by trigono…
Deformed sine-Gordon (DSG) models $\partial_ξ\partial_η\, w + \frac{d}{dw}V(w) = 0$, with $V(w)$ being the deformed potential, are considered in the context of the Riccati-type pseudopotential approach. A compatibility condition of the deformed system of Riccati-type equations reproduces the equation of motion of the DSG models. Then, we provide a pair of linear systems of equations for DSG model, and provide an infinite tower of non-local conservation laws. Through a direct construction and supported by numerical simulations of soliton scatterings, we show that the DSG models, which have rece…
A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)（阿·伊·阿里哈尼扬国家科学实验室（叶里万物理研究所））；Departamento de Física de Partículas, Universidad de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学粒子物理学系）；Instituto Galego de Física de Altas Enerxias (IGFAE)（加利西亚高能物理研究所）
Université de Genève（日内瓦大学）；CERN（欧洲核子研究中心）；SISSA（的里雅斯特国际高等研究学校）；INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；Institute for Geometry and Physics, IGAP（几何与物理研究所）
