We study an example of higher-order field-theoretic model with an eighth-degree polynomial potential -- the $φ^8$ model. We show that for some certain ratios of constants of the potential, the problem of finding kink-type solutions in $(1+1)$-dimensional space-time reduces to solving algebraic equations. For two different ratios of the constants, which determine positions of the vacua, we obtained explicit formulas for kinks in all topological sectors. The properties of the obtained kinks are also studied -- their masses are calculated, and the excitation spectra which could be responsible for the appearance of resonance phenomena in kink-antikink scattering are found.
We obtain exact solutions for kinks in $ϕ^{8}$, $ϕ^{10}$ and $ϕ^{12}$ field theories with degenerate minima, which can describe a second-order phase transition followed by a first-order one, a succession of two first-order phase transitions and a second-order phase transition followed by two first-order phase transitions, respectively. Such phase transitions are known to occur in ferroelastic and ferroelectric crystals and in meson physics. In particular, we find that the higher-order field theories have kink solutions with algebraically-decaying tails and also asymmetric cases with mixed expo…
Confining kinks. $ζ$-regularized one-loop kink mass shifts in exotic field theories
Universidad de Santiago de Chile（圣地亚哥智利大学）；Universidad de Salamanca（萨拉曼卡大学）；Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile（智利南方大学物理与数学科学研究所）；IPNP - Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院）
We determine the semiclassical energy levels for the ϕ^4 field theory in the broken symmetry phase on a 2D cylindrical geometry with antiperiodic boundary conditions by quantizing the appropriate finite--volume kink solutions. The analytic form of the kink scaling functions for arbitrary size of the system allows us to describe the flow between the twisted sector of c=1 CFT in the UV region and the massive particles in the IR limit. Kink-creating operators are shown to correspond in the UV limit to disorder fields of the c=1 CFT. The problem of the finite--volume spectrum for generic 2D Landau…
We present several one-parameter family of higher order field theory models some of which admit explicit kink solutions with an exponential tail while others admit explicit kink solutions with a power-law tail. Various properties of these families of kink solutions are examined in detail. In particular for models harboring kink solutions with a power-law tail, we show that there is no gap between the zero mode and the beginning of the continuum in the kink stability potential. Further, by applying the recent Manton formalism, we provide estimates for the kink-kink and antikink-kink acceleratio…
In this talk we discuss an elementary derivation of the semi-classical spectrum of neutral particles in two field theories with kink excitations. We also show that, in the non-integrable cases, each vacuum state cannot generically support more than two stable particles, since all other neutral exitations are resonances, which will eventually decay.
Oscillons are time-dependent, localized in space, extremely long-lived states in nonlinear scalar-field models, while kinks are topological solitons in one spatial dimension. In the present work, we show new classes of oscillons and oscillating kinks in a system of two nonlinearly coupled scalar fields in $1 + 1$ spatiotemporal dimensions. The solutions contain a control parameter, the variation of which produces oscillons and kinks with a flat-top shape. The model finds applications to condensed matter, cosmology, and high-energy physics.
We consider a family of field-theoretic models with a real scalar field in (1+1)-dimensional space-time. The field dynamics in each model is determined by a polynomial potential with two degenerate minima. We obtain exact general formulas for kink solutions with power-law asymptotic behavior. We also write out formulas for the asymptotics of all found kinks. In addition, we analyze some other properties of the obtained kinks: stability potentials, zero modes, positions of the centers of mass.
We analyze the evolution of the effective potential and the particle spectrum of two-parameter families of non-integrable quantum field theories. These theories are defined by deformations of conformal minimal models M_m by using the operators Phi_{1,3}, Phi_{1,2} and Phi_{2,1}. This study extends to all minimal models the analysis previously done for the classes of universality of the Ising, the Tricritical Ising and the RSOS models. We establish the symmetry and the duality properties of the various models also identifying the limiting theories that emerge when m goes to infinity.
In this paper we present an elementary derivation of the semi-classical spectrum of neutral particles in a field theory with kink excitations. In the non-integrable cases, we show that each vacuum state cannot generically support more than two stable particles, since all other neutral exitations are resonances, which will eventually decay. A phase space estimate of these decay rates is also given. This shows that there may be a window of values of the coupling constant where a particle with higher mass is more stable than the one with lower mass. We also discuss the crossing symmetry propertie…
The path is explored between one-dimensional scattering through Dirac-$δ$ walls and one-dimensional quantum field theories defined on a finite length interval with Dirichlet boundary conditions. It is found that two $δ$'s are related to the Casimir effect whereas two $δ$'s plus the first transparent P$\ddot{\rm o}$sch-Teller well arise in the context of the sine-Gordon kink fluctuations, both phenomena subjected to Dirichlet boundary conditions. One or two delta wells will be also explored in order to describe absorbent plates, even though the wells lead to non unitary Quantum Field Theories.
We consider the Ising Field Theory (IFT), and the 3-state Potts Field Theory (PFT), which describe the scaling limits of the two- dimensional lattice q-state Potts model with q=2, and q=3, respectively. At zero magnetic field h=0, both field theories are integrable away from the critical point, have q degenerate vacua in the ferromagnetic phase, and q(q-1) particles of the same mass - the kinks interpolating between two different vacua. Application of a weak magnetic field induces confinement of kinks into bound states - the mesons (for q =2,3) consisting predominantly of two kinks, and baryon…
In this paper we study the possibility of constructing two-field models from one-field models. The idea is to start with a given one-field model and use the deformation procedure to generate another one-field model, and then couple the two one-field models nontrivially, to get to a two-field model, together with some explicit topological solutions. We show with several distinct examples that the procedure works nicely and can be used generically.
We study kinks in a wide class of noncommutative (NC) field theories. We find rich structure of the static kinks in DBI type NC tachyon action for an unstable D$p$-brane with general constant open string metric and NC parameter. Among which thick topological BPS NC kink and tensionless half-kink are particularly intriguing. Reproduction of the correct decent relation between D$p$ and D$(p-1)$ lets us interpret the obtained NC kinks as codimension-one D-brane and its composites. If we turn on DBI type NC U(1) gauge field on an unstable D2-brane, only constant field strength is allowed by gauge …
In the paper, we make use of Manton's analytical method to investigate the force between kink and the anti-kink with large distance in $1+1$ dimensional field theory. The related potential has infinite order corrections of exponential pattern, and coefficients for each order are determined. These coefficients can also be obtained by solving the equation of the fluctuation around the vacuum. At the lowest order, the kink lattice represents the Toda lattice. With higher order correction terms, the kink lattice can represent one kind of the generic Toda lattice. With only two sites, the kink latt…
We continue the investigation of supersymmetric extensions of field theories with a non-standard kinetic term (K field theories) resumed recently. Concretely, for K field theories which allow for kink or compacton solutions in 1+1 dimensions, i.e., for domain walls in a higher-dimensional context, we find a simple supersymmetric extension such that the boson field still has the kink solution, and the field equation for the fermion in the kink background is linear and is solved by the first spatial derivative of the kink, as is the case in the corresponding standard supersymmetric theories. Thi…
We consider a class of integrable quantum field theories in 1+1 dimensions whose classical equations have kink solutions with internal collective coordinates that transform under a non-abelian symmetry group. These generalised sine-Gordon theories have been shown to be related to the world sheet theory of the string in the AdS/CFT correspondence. We provide a careful analysis of the boundary conditions at spatial infinity complicated by the fact that they are defined by actions with a WZ term. We go on to describe the local and non-local charges carried by the kinks and end by showing that the…
In this Letter, we address the {long-range interaction} between kinks and antikinks, as well as kinks and kinks, in $φ^{2n+4}$ field theories for $n>1$. The kink-antikink interaction is generically attractive, while the kink-kink interaction is generically repulsive. We find that the force of interaction decays with the $(\frac{2n}{n-1})$th power of their separation, and we identify the general prefactor for {\it arbitrary} $n$. Importantly, we test the resulting mathematical prediction with detailed numerical simulations of the dynamic field equation, and obtain good agreement between theory …
We study collisions of coherent structures in higher-order field-theoretic models, such as the $ϕ^8$, $ϕ^{10}$ and $ϕ^{12}$ ones. The main distinguishing feature, of the example models considered herein, is that the collision arises due to the long-range interacting algebraic tails of these solitary waves. We extend the approach to suitably initialize the relevant kinks, in the additional presence of finite initial speed, in order to minimize the dispersive wave radiation potentially created by their slow spatial decay. We find that, when suitably initialized, these models still feature the mu…
Quantum-disordering a discrete-symmetry breaking state by condensing domain-walls can lead to a trivial symmetric insulator state. In this work, we show that if we bind a 1D representation of the symmetry (such as a charge) to the intersection point of several domain walls, condensing such modified domain-walls can lead to a non-trivial symmetry-protected topological (SPT) state. This result is obtained by showing that the modified domain-wall condensed state has a non-trivial SPT invariant -- the symmetry-twist dependent partition function. We propose two different kinds of field theories tha…
We examine solitons in theories with heavy fermions. These ``quantum'' solitons differ dramatically from semi-classical (perturbative) solitons because fermion loop effects are important when the Yukawa coupling is strong. We focus on kinks in a $(1+1)$--dimensional $ϕ^4$ theory coupled to fermions; a large-$N$ expansion is employed to treat the Yukawa coupling $g$ nonperturbatively. A local expression for the fermion vacuum energy is derived using the WKB approximation for the Dirac eigenvalues. We find that fermion loop corrections increase the energy of the kink and (for large $g$) decrease…
We discuss finite regions of the deconfining phase of a confining gauge theory (plasma balls/kinks) as solitons of the large $N$, long wavelength, effective Lagrangian of the thermal gauge theory expressed in terms of suitable order parameters. We consider a class of confining gauge theories whose effective Lagrangian turns out to be a generic 1 dim. unitary matrix model. The dynamics of this matrix model can be studied by an exact mapping to a non-relativistic many fermion problem on a circle. We present an approximate solution to the equations of motion which corresponds to the motion (in Eu…
In this paper we show that in field theories with topologically stable kinks and flat directions in their potential, a so-called dynamical vacuum selection (DVS) takes place in the non-trivial, soliton sector of the theory. We explore this DVS mechanism using a specific model. For this model we show that there is only a static kink solution when very specific boundary conditions are met, very similar to the case of vortices in two dimensions. In the case of other boundary conditions a scalar cloud is expelled to infinity, leaving a static kink behind. Other circumstances under which DVS may or…
The moduli space approximation to kink dynamics permits a relativistic generalization if the Derrick scaling parameter is used as a collective coordinate. We develop a perturbative approach to the resulting relativistic moduli space by expanding the Derrick scaling parameter about unity and treating the higher-order Derrick modes as new degrees of freedom. This approach allows us to resolve (coordinate) singularities order-by-order, and systematically incorporates relativistic corrections {\it perturbatively} in kink scattering. It gives an excellent description of kink-antikink collisions in …
In this work we consider kink-antikink collisions for some classes of $(1,1)$-dimensional nonlinear models. We are particularly interested to investigate in which aspect the presence of a general kinetic content in the Lagrangian could be revealed in a collision process. We consider a particular class of models known as twin theories, where different models lead to same solutions for the equations of motion and same energy density profile. The theories can be distinguished in the level of linear stability of defect structure. We study a class of k-defect theories depending on a parameter $M$ w…
A (1+1)-dimensional quantum field theory with a degenerate vacuum (in infinite volume) can contain particles, known as kinks, which interpolate between different vacua and have nontrivial restrictions on their multi-particle Hilbert space. Assuming such a theory to be integrable, we show how to calculate the multi-kink energy levels in finite volume given its factorizable $S$-matrix. In massive theories this can be done exactly up to contributions due to off-shell and tunneling effects that fall off exponentially with volume. As a first application we compare our analytical predictions for the…
We study static kink configurations in a type of two-dimensional higher derivative scalar field theory whose Lagrangian contains second-order derivative terms of the field. The linear fluctuation around arbitrary static kink solutions is analyzed. We find that, the linear spectrum can be described by a supersymmetric quantum mechanics problem, and the criteria for stable static solutions can be given analytically. We also construct a superpotential formalism for finding analytical static kink solutions. Using this formalism we first reproduce some existed solutions and then offer a new solutio…
We continue to study the BPS spectrum of the N=(2,2) CP(N-1) model with the Z_N-symmetric twisted mass terms. We focus on analysis of the "extra" towers found previously in [1], and compare them to the states that can be identified in the quasiclassical domain. Exact analysis of the strong-coupling states shows that not all of them survive when passing to the weak-coupling domain. Some of the states decay on the curves of the marginal stability (CMS). Thus, not all strong-coupling states can be analytically continued to weak coupling to match the observable bound states. At weak coupling, we c…
Two-dimensional scalar field theories with spontaneous symmetry breaking subject to the action of Jackiw-Teitelboim gravity are studied. Solutions for the $ϕ^4$ and sine-Gordon self-gravitating kinks are presented, both for general gravitational coupling and in the perturbative regime. The analysis is extended to deal with a hierarchy of kinks related to transparent Pöschl-Teller potentials
We present a computational analysis of the long-range interactions of solitary waves in higher-order field theories. Our vehicle of choice is the $φ^8$ field theory, although we explore similar issues in example $φ^{10}$ and $φ^{12}$ models. In particular, we discuss the fundamental differences between the latter higher-order models and the standard $φ^4$ model. Upon establishing the power-law asymptotics of the model's solutions' approach towards one of the steady states, we make the case that such asymptotics require particular care in setting up multi-soliton initial conditions. A naive imp…
We provide examples of a large class of one dimensional higher order field theories with kink solutions which asymptotically have a power-law tail either at one end or at both ends. We provide analytic solutions for the kinks in a few cases but mostly provide implicit solutions. We also provide examples of a family of potentials with two kinks, both of which have power law tails either at both ends or at one end. In addition, we show that for kinks with a power law tail at one end or both the ends, there is no gap between the zero mode and the continuum of the corresponding stability equation.…
Scattering of kinks in Frankensteinian potentials: Kinks as bubbles of exotic mass and phase transitions in oscillon production
Institute of Physics, Silesian University in Opava（奥帕瓦西里西亚大学物理研究所）；Research Centre for Theoretical Physics and Astrophysics, Institute of Physics, Silesian University in Opava（奥帕瓦西里西亚大学物理研究所理论物理与天体物理研究中心）
Darboux transformations are employed in construction and analysis of Dirac Hamiltonians with pseudoscalar potentials. By this method, we build a four parameter class of reflectionless systems. Their potentials correspond to composition of complex kinks, also known as twisted kinks, that play an important role in the $1+1$ Gross-Neveu and Nambu-Jona-Lasinio field theories. The twisted kinks turn out to be multi-solitonic solutions of the integrable AKNS hierarchy. Consequently, all the spectral properties of the Dirac reflectionless systems are reflected in a non-trivial conserved quantity, whi…
We show how detailed properties of a kink in quantum field theory can be extracted from field correlation functions. This makes it possible to study quantum kinks in a fully non-perturbative way using Monte Carlo simulations. We demonstrate this by calculating the kink mass as well as the spectrum and approximate wave functions of its excitations. This way of measuring the kink mass has clear advantages over the existing approaches based on creation and annihilation operators or the kink free energy. Our methods are straightforward to generalise to more realistic theories and other defect type…
Recent programs on conformal bootstrap suggest an empirical relationship between the existence of non-trivial conformal field theories and non-trivial features such as a kink in the unitarity bound of conformal dimensions in the conformal bootstrap equations. We report the existene of non-trivial kinks in the unitarity bound of scalar operators in the adjoint representation of the $SU(N)$ symmetric conformal field theories. They have interesting properties (1) the kinks exist in $d<6$ dimensions (2) the location of kinks are when the unitarity bound hits the space-time dimension $d$ (3) there …
Solitons in classical field theories correspond to states in quantum field theories. If the spatial dimension is infinite, then momentum eigenstates are not normalizable. This leads to infrared divergences, which are generally regularized via wave packets or by compactification. However, in some applications both possibilities are undesirable. In the present note, we introduce a finite inner product on translation-invariant kink states that allows us to compute probabilities involving these nonnormalizable states. Essentially, it is the quotient of the usual inner product by the translation gr…
Infrared fixed points of gauge theories provide intriguing targets for the modern conformal bootstrap program. In this work we provide some preliminary evidence that a family of gauged fermionic CFTs saturate bootstrap bounds and can potentially be solved with the conformal bootstrap. We start by considering the bootstrap for $SO(N)$ vector 4-point functions in general dimension $D$. In the large $N$ limit, upper bounds on the scaling dimensions of the lowest $SO(N)$ singlet and traceless symmetric scalars interpolate between two solutions at $Δ=D/2-1$ and $Δ=D-1$ via generalized free field th…
I use the numerical values of the generalised Glaisher-Kinkelin-Bendersky (GKB) constants to give numerical values for the derivatives of the Hurwitz zeta function at negative integers, rather than the other way round. I point out that both Glaisher's numerical approach and Bendersky's recursion for the generalised gamma function were anticipated by Jeffery in 1862 who gave the value of the second constant as an example. I therefore propose that GKB become GKBJ.
We consider topological solitons in the CP^n sigma models in two space dimensions. In particular, we study "kinks", which are independent of one coordinate up to a rotation of the target space, and "chains", which are periodic in one coordinate up to a rotation of the target space. Kinks and chains both exhibit constituents, similar to monopoles and calorons in SU(n) Yang-Mills-Higgs and Yang-Mills theories. We examine the constituent structure using Lie algebras.
We investigate scalar field theories in the multifield scenario, focusing mainly on the possibility to smoothly build internal structure and asymmetry for kinks and domain walls. The procedure requires the inclusion of an extra field which is associated to a function that modifies the dynamics of the other fields. We investigate minimum energy configurations, which support first order equations compatible with the equations of motion. The extra field allows a transition which is guided by a parameter that connects the standard solution to another one, geometrically constrained, mimicking the e…
Kink-antikink scattering in the $ϕ^4$ model is investigated in the limit when the static inter-soliton force vanishes. We observe the formation of spectral walls and, further, identify a new phenomenon, the vacuum wall, whose existence gives rise to a bouncing structure for the annihilating solitons. Furthermore, we discover higher order spectral walls, i.e., spectral walls which form when higher harmonics enter the continuous spectrum. These higher order spectral walls not only deform the soliton trajectories, they also can be observed easily as very intense radiation bursts.
Recently a linearized perturbation theory has been formulated for soliton sectors of quantum field theories. While it is more economical than alternative formalisms, such as collective coordinates, it is currently limited to solitons which stay close to a base point, about which the theory is linearized. As a result, so far this formalism has only been applied to stationary solitons. In spite of this limitation, we construct kink states with fixed nonzero momenta and also moving, normalizable kink wave packets. The former are nonnormalizable, coherent superpositions of kinks at all spatial pos…
In this article, we study kink soliton configurations in interacting scalar field theories containing two fields without $SO(2)$ invariance. We study a class of such theories, the well-known Montonen-Sarker-Trullinger-Bishop model is one of them. These models are interesting since the $U(1)$ current is not conserved in them due to the presence of explicit symmetry breaking terms in the action. The existence of kink soliton configurations is shown in terms of a system of first-order ordinary differential equations. Although $U(1)$ current in these models are non-conserved, our approach is gener…
We review the recently developed supersymmetric extensions of field theories with non-standard kinetic terms (so-called K field theories) in two an three dimensions. Further, we study the issue of topological defect formation in these supersymmetric theories. Specifically, we find supersymmetric K field theories which support topological kinks in 1+1 dimensions as well as supersymmetric extensions of the baby Skyrme model for arbitrary nonnegative potentials in 2+1 dimensions.
We compute semiclassical corrections to the energy density of kinks in $ϕ^4$ theory and of solitons in the sine-Gordon model in $1+1$ dimensions, using local and covariant renormalization techniques from quantum field theory in curved spacetimes. For the semiclassical correction to the energy, we recover the known results. Our analysis highlights a subtlety in the definition of a conserved stress tensor for scalar field theories in $1+1$ dimension.
We study the supersymmetric kink with higher derivative and momentum cut-off regularization schemes. We introduce the new momentum cut-off regularization scheme which we call ``generalized momentum cut-off''. A new, explicit computation for the central charge anomaly for this scheme is described in detail. The calculation of the first order mass corrections for the bosonic and supersymmetric kink within the momentum cut-off is presented in hep-th/0010051, so that one can compare the one-loop central charge and mass computed independently within the same regularization setup. We confirm that th…
It was recently proposed a novel discretization for nonlinear Klein-Gordon field theories in which the resulting lattice preserves the topological (Bogomol'nyi) lower bound on the kink energy and, as a consequence, has no Peierls-Nabarro barrier even for large spatial discretizations (h~1.0). It was then suggested that these ``topological discrete systems'' are a natural choice for the numerical study of continuum kink dynamics. Giving particular emphasis to the phi^4 theory, we numerically investigate kink-antikink scattering and breather formation in these topological lattices. Our results i…
We investigate the existence and properties of kink-like solitons in a class of models with two interacting scalar fields. In particular, we focus on models that display both double and single-kink solutions, treatable analytically using the Bogomol'nyi--Prasad--Sommerfield bound (BPS). Such models are of interest in applications that include Skyrmions and various superstring-motivated theories. Exploring a region of parameter space where the energy for very different spatially-bound configurations is degenerate, we show that a newly-proposed momentum-space entropic measure called Configuratio…
