For a single free scalar field in $d \geq 2$ dimensions, almost all the unitary conformal defects must be `trivial' in the sense that they cannot hold interesting dynamics. The only possible exceptions are monodromy defects in $d \geq 4$ and co-dimension three defects in $d \geq 5$. As an intermediate result we show that the $n$-point correlation functions of a conformal theory with a generalized free spectrum must be those of the generalized free theory.
We study the Euclidean effective action and the full fermion propagator for a Dirac field in the presence of a scalar field with a domain wall defect, in 2+1 dimensions. We include quantum effects due to both fermion and scalar field fluctuations, in a one-loop approximation. The results are interpreted in terms of the quantum stability of the zero mode solution. We also study, for this system, the induced `inertial' electric field for the fermions on the defect, due to the quantum fluctuations of the scalar field.
We consider defect operators in scalar field theories in dimensions $d=4-ε$ and $d=6-ε$ with self-interactions given by a general marginal potential. In a double scaling limit, where the bulk couplings go to zero and the defect couplings go to infinity, the bulk theory becomes classical and the quantum defect theory can be solved order by order in perturbation theory. We compute the defect $β$ functions to two loops and study the Renormalization Group flows. The defect fixed points can move and merge, leading to fixed point annihilation; and they exhibit a remarkable factorization property whe…
In this paper, we analyzed the relativistic quantum motion of a charged scalar particles in the presence of a Aharonov Bohm and Coulomb potentials in the spacetimes produced by an idealized cosmic strings and global monopoles.
The computation of the effect of a simple monodromy defect in the case of a sphere with twisted boundary conditions is revisited and streamlined using earlier calculations for a similar system. Compact and explicit expressions are found for arbitrary integer dimensions. Comments on other work are made.
In this paper we use the deformation procedure introduced in former work on deformed defects to investigate several new models for real scalar field. We introduce an interesting deformation function, from which we obtain two distinct families of models, labeled by the parameters that identify the deformation function. We investigate these models, which identify a broad class of polynomial interactions. We find exact solutions describing global defects, and we study the corresponding stability very carefully.
In this work we review some features of topological defects in field theory models for real scalar fields. We investigate topological defects in models involving one and two or more real scalar fields. In models involving a single field we examine two different subclasses of models, which support one or more topological defects. In models involving two or more real scalar fields, we explore the presence of defects that live inside topological defects, and junctions and networks of defects. In the case of junctions of defects we investigte structures that simulate nanotubes and fulerenes. Our i…
We describe conformal defects of $p$ dimensions in a free scalar theory on a $d$-dimensional flat space as boundary conditions on the conformally flat space $\mathbb{H}^{p+1}\times \mathbb{S}^{d-p-1}$. We classify two types of boundary conditions, Dirichlet type and Neumann type, on the boundary of the subspace $\mathbb{H}^{p+1}$ which correspond to the types of conformal defects in the free scalar theory. We find Dirichlet boundary conditions always exist while Neumann boundary conditions are allowed only for defects of lower codimensions. Our results match with a recent classification of the…
In this work we offer an approach to enlarge the number of exactly solvable models with two real scalar fields in (1+1)D. We build some new two-field models, and obtain their exact orbits and exact or numerical field configurations. It is noteworthy that a model presenting triple-kinks and double-flat-top lumps is among those new models.
We study the operator product expansion (OPE) for scalar conformal defects of any codimension in CFT. The OPE for defects is decomposed into "defect OPE blocks", the irreducible representations of the conformal group, each of which packages the contribution from a primary operator and its descendants. We use the shadow formalism to deduce an integral representation of the defect OPE blocks. They are shown to obey a set of constraint equations that can be regarded as equations of motion for a scalar field propagating on the moduli space of the defects. By employing the Radon transform between t…
We consider a complex scalar field in (p+3)-dimensional bulk with a negative cosmological constant and study global vortices in two extra-dimensions. We reexamine carefully the coupled scalar and Einstein equations, and show that the boundary value of scalar amplitude at infinity of the extra-dimensions should be smaller than vacuum expectation value. The brane world has a cigar-like geometry with an exponentially decaying warp factor and a flat thick p-brane is embedded. Since a coordinate transformation identifies the obtained brane world as a black p-brane world bounded by a horizon, this s…
We develop a general procedure to deal with defect structures in generalized models, described by a single real scalar field, in (1,1) spacetime dimensions. The models that we consider have the standard kinetic and potential contributions modified to include corrections that depend on a single small parameters, used to control modification on the kinematics and the potential. We start with standard model that engenders stable defect structures, and we show how to obtain new structures for the generalized models. We examine distinct aspects of the new deformed solutions, including linear stabil…
We investigate the localization of modes on the worldvolume of a p-brane embedded in p+d+1-dimensional spacetime. The p-brane here is such that its profile is regarded as a scalar global defect and the localized modes are scalar modes that come from the fluctuations around such defect. The effective action on the brane is computed and the induced potentials are typically phi^4-type potentials that are flatter for lower d-dimensions. We also make a connection of such scalar global defects with black p-branes in certain limits.
The influence of a Lorentz-violation on soliton solutions generated by a system of two coupled scalar fields is investigated. Lorentz violation is induced by a fixed tensor coefficient that couples the two fields. The Bogomol'nyi method is applied and first-order differential equations are obtained whose solutions minimize energy and are also solutions of the equations of motion. The analysis of the solutions in phase space shows how the stability is modified with the Lorentz violation. It is shown explicitly that the solutions preserve linear stability despite the presence of Lorentz violatio…
We study quantum fluctuations of a free massless scalar field during inflation in the presence of a point, line, or plane defect such as a black hole, cosmic string, or domain wall, using a perturbative expansion in powers of small defect parameters. We provide results for the scalar two-point correlation functions that show explicitly a small violation of translational invariance during inflation.
We investigate the effects of small static defects in the spacetime manifold. The presence of the defects leads to a modification of the scalar field two-point function in Klein-Gordon theory. We calculate the energy-momentum tensor and discuss the possible mass generation for the scalar field in single and multiple defect spacetimes. We also extend these results to the photon field and show that, as a result of the interaction with the defects, the photon dispersion relations are modified.
In this work we investigate the role of the symmetry of the Lagrangian on the existence of defects in systems of coupled scalar fields. We focus attention mainly on solutions where defects may nest defects. When space is non-compact we find topological BPS and non-BPS solutions that present internal structure. When space is compact the solutions are nontopological sphalerons, which may be nested inside the topological defects. We address the question of classical stability of these topological and nontopological solutions and investigate how the thermal corrections may modify the classical sce…
We propose a new way to build networks of defects. The idea takes advantage of the deformation procedure recently employed to describe defect structures, which we use to construct networks, spread from small rudimentary networks that appear in simple models of scalar fields.
In this work we introduce new scalar field models and study the defect solutions they may engender. The investigation is based on the deformation procedure, which greatly simplify the calculations, leading us to new models together with the corresponding solutions in a simple and powerful manner.
We have considered the localization of resonant bosonic states described by a scalar field $Φ$ trapped in tube-like topological defects. The tubes are formed by radial symmetric defects in $(2,1)$ dimensions, constructed with two scalar fields $ϕ$ and $χ$, and embedded in the $(3,1)-$dimensional Minkowski spacetime. The general coupling between the topological defect and the scalar field $Φ$ is given by the potential $ηF(ϕ,χ)Φ^2$. After a convenient decomposition of the field $Φ$, we find that the amplitudes of the radial modes satisfy Schrödinger-like equations whose eigenvalues are the masse…
Topological defects and scalar field modes in cosmological backgrounds
Institute of Physics, Yerevan State University（耶烈万国立大学物理研究所）；CANDLE Synchrotron Research Institute（CANDLE 同步辐射研究所）；Institute of Applied Problems of Physics NAS RA（亚美尼亚国家科学院应用物理问题研究所）
A topological defect in the form of the Abrikosov-Nielsen-Olesen vortex in a space of arbitrary dimension is considered as a gauge-flux-carrying tube that is impenetrable for quantum matter. Charged scalar matter field is quantized in the vortex background with the perfectly rigid (Neumann) boundary condition imposed at the side surface of the vortex. We show that a current circulating around the vortex is induced in the vacuum, if the Compton wavelength of the matter field exceeds the transverse size of the vortex considerably. The vacuum current is periodic in the value of the gauge flux of …
In this paper, we demonstrate that a phenomenon described as "topological inflation" during which inflation occurs inside the core of topological defects, has a non-topological counterpart. This appears in a simple set-up containing Einstein gravity coupled minimally to an electromagnetic field as well as a self-interacting, complex valued scalar field. The U(1) symmetry of the model is unbroken and leads to the existence of globally regular solutions, so-called boson stars, that develop a horizon for sufficiently strong gravitational coupling. We also find that the same phenomenon exists for …
We study the anomalous dimension of the cusped Maldacena-Wilson line in planar $\mathcal{N} = 4$ Yang-Mills theory with scalar insertions using the Quantum Spectral Curve (QSC) method. In the straight line limit we interpret the excited states of the QSC as insertions of scalar operators coupled to the line. Such insertions were recently intensively studied in the context of the one-dimensional defect CFT. We compute a five-loop perturbative result analytically at weak coupling and the first four orders in the $1/\sqrtλ$ expansion at strong coupling, confirming all previous analytic results. I…
Boundaries and defects in conformal field theories at finite temperature
Università di Parma（帕尔马大学）；INFN Gruppo Collegato di Parma（意大利国家核物理研究所帕尔马协作组）；Dipartimento di Fisica, Università di Torino（都灵大学物理系）；INFN, Sezione di Torino（意大利国家核物理研究所都灵分部）
In this paper we analyse the relativistic quantum motion of a charged spin-0 particle in the presence of a dyon, Aharonov-Bohm magnetic field and scalar potential, in the spacetimes produced by an idealized cosmic string and global monopole. In order to develop this analysis, we assume that the dyon and the Aharonov-Bohm magnetic field are superposed to both gravitational defects. Two distinct configurations for the scalar potential, $S(r)$, are considered: $i)$ the potential proportional to the inverse of the radial distance, i.e., $S\propto1/r$, and $ii)$ the potential proportional to this d…
We show that the Gukov-Witten monodromy defects of supersymmetric Yang-Mills theory can be realized in perturbative string theory by considering an orbifold background of the Kanno-Tachikawa type and placing stacks of fractional D3-branes whose world-volume partially extends along the orbifold directions. In particular, we show that turning on a constant background value for some scalar fields in the closed string twisted sectors induces a non-trivial profile for the gauge field and one of the complex scalars of the world-volume theory, and that this profile exactly matches the singular behavi…
In this work we consider $(1,1)-$dimensional resonant Dirac fermionic states on tube-like topological defects. The defects are formed by rings in $(2,1)$ dimensions, constructed with two scalar field $ϕ$ and $χ$, and embedded in the $(3,1)-$dimensional Minkowski spacetime. The tube-like defects are attained from a lagrangian density explicitly dependent with the radial distance $r$ relative to the ring axis and the radius and thickness of the its cross-section are related to the energy density. For our purposes we analyze a general Yukawa-like coupling between the topological defect and the fe…
In these Lectures a method is described to analyze the effect of quantum fluctuations on topological defect backgrounds up to the one-loop level. The method is based on the spectral heat kernel/zeta function regularization procedure, and it is first applied to various types of kinks arising in several deformed linear and non-linear sigma models with different numbers of scalar fields. In the second part, the same conceptual framework is constructed for the topological solitons of the planar semilocal Abelian Higgs model, built from a doublet of complex scalar fields and one U(1) gauge field.
In this note, we study the eigenvectors and the scalar products the integrable long-range deformation of a XXX spin chain which is solved exactly by algebraic Bethe ansatz, and it coincides in the bulk with the Inozemtsev spin chain. At the closing point it contains a defect which effectively removes the wrapping interactions. Here we concentrate on determining the defect term for the first non-trivial order in perturbation in the deformation parameter and how it affects the Bethe ansatz equations. Our study is motivated by the relation with the dilatation operator of the N = 4 gauge theory in…
This work deals with the construction of networks of topological defects in models described by a single complex scalar field. We take advantage of the deformation procedure recently used to describe kinklike defects in order to build networks of topological defects, which appear from complex field models with potentials that engender a finite number of isolated minima, both in the case where the minima present discrete symmetry, and in the non symmetric case. We show that the presence of symmetry guide us to the construction of regular networks, while the non symmetric case gives rise to irre…
We investigate a stability equation involving two-component eigenfunctions which is associated with a potential model in terms of two coupled real scalar fields, which presents non BPS topological defect.
We make an analysis about several aspects of localization of a scalar field and a Kalb-Ramond gauge field in a specific four dimensional AdS membrane embedded in a five dimensional space-time. The membrane is generated from a deformation of the $λϕ^4$ potential and belongs to a new class of defect solutions. The study of deformed defects is important because they contain internal structures and these may have implications to the way the background space-time is constructed and the way its curvature behaves. The main objective is to observe the contributions of the deformation procedure to the …
We study multipoint correlators of protected scalars on the Maldacena-Wilson line in $\mathcal{N}=4$ SYM. Working at weak coupling in the planar limit, we derive an explicit recursion relation that captures next-to-leading order correlators with an arbitrary number of insertions of the fundamental scalar field. By pinching fundamental scalars together, we can build composite protected operators with higher values of the R-charge. Our result then encompasses arbitrary $n$-point correlators of protected operators with arbitrary weight. As a demonstration of our method, we give explicit formulae …
We develop a group theoretical formalism to study correlation functions in defect conformal field theory, with multiple insertions of bulk and defect fields. This formalism is applied to construct the defect conformal blocks for three-point functions of scalar fields. Starting from a configuration with one bulk and one defect field, for which the correlation function is determined by conformal symmetry, we explore two possibilities, adding either one additional defect or bulk field. In both cases it is possible to express the blocks in terms of classical hypergeometric functions, though the ca…
In this paper we deal with defects inside defects in systems of two scalar fields in 3+1 dimensions. The systems we consider are defined by potentials containing two real scalar fields, and so we are going to investigate domain ribbons inside domain walls. After introducing some general comments on the possibility of finding defects that support internal structure in two specific systems, we introduce thermal effects to show how the picture for domain walls hosting domain ribbons appears at high temperature.
We consider conformal defects with spins under the rotation group acting on the transverse directions. They are described in the embedding space formalism in a similar manner to spinning local operators, and their correlation functions with bulk and defect local operators are determined by the conformal symmetry. The operator product expansion (OPE) structure of spinning conformal defects is examined by decomposing it into the spinning defect OPE block that packages all the contribution from a conformal multiplet. The integral representation of the block derived in the shadow formalism is faci…
We study k-defects - topological defects in theories with more than two derivatives and second-order equations of motion - and describe some striking ways in which these defects both resemble and differ from their analogues in canonical scalar field theories. We show that, for some models, the homotopy structure of the vacuum manifold is insufficient to establish the existence of k-defects, in contrast to the canonical case. These results also constrain certain families of DBI instanton solutions in the 4-dimensional effective theory. We then describe a class of k-defect solutions, which we du…
In this thesis, we study interactions between topological defects in two-dimensional spacetimes. These defects are called kinks. They are solutions of scalar field theories with localized energy which propagate without losing its shape. In order to understand the resonance phenomenon exhibited by those models, we built a toy model where the kink's vibrational mode turns into a quasinormal mode. This causes the suppression of resonance windows and, consequently, its fractal structure is lost. Considering a higher order polynomial as the scalar field potential, we find kinks with long-range tail…
Explicit polynomial forms for Rényi and entanglement entropies are given on even --dimensional spheres which possess a codimension--2 U(1) monodromy defect. Free scalar and Dirac fields are treated and higher-derivative propagation operators employed. The central charge, $C_T$, is also calculated. Comparison with existing results is made and it is shown how these can be obtained from the values here.
We show that a dispiration (a disclination plus a screw dislocation) polarizes the vacuum of a scalar field giving rise to an energy momentum tensor which, as seen from a local inertial frame, presents non vanishing off-diagonal components. The results may have applications in cosmology (chiral cosmic strings) and condensed matter physics (materials with linear defects).
This work deals with the presence of defect structures in models described by real scalar field in a diversity of scenarios. The defect structures which we consider are static solutions of the equations of motion which depend on a single spatial dimension. We search for different models, which support the same defect solution, with the very same energy density. We work in flat spacetime, where we introduce and investigate a new class of models. We also work in curved spacetime, within the braneworld context, with a single extra dimension of infinite extent, and there we show how the brane is f…
We introduce a method to obtain deformed defects starting from a given scalar field theory which possesses defect solutions. The procedure allows the construction of infinitely many new theories that support defect solutions, analytically expressed in terms of the defects of the original theory. The method is general, valid for both topological and non-topological defects, and we show how it extends to quantum mechanics, and how it works when the scalar field couples to fermions. We illustrate the general procedure with several examples, which support kink-like or lump-like defects.
Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave functions of an integrable multi-particle Calogero-Sutherland problem. This generalizes a recent observation in 1602.01858 and makes extensive mathematical results from the modern theory of multi-variable hypergeometric functions available for studies of conformal defects. Applications range from several new relations with scalar four-point blocks to a Eucl…
We explore perturbations to a kink-like (codimension 1) topological defect whose world brane is $AdS_{q}$ embedded into $AdS_{q+1}$. Previously, we found solutions in the limit the mass of the scalar field vanishes. In this article we extend a calculation previously done in $AdS_{2}$ to higher-dimensional embedding spaces and find that all perturbations to the mass of the field are stable to first order as expected in a theory with topological defects. We find that the equation of motion to the correction strongly resembles a problem well-known in quantum mechanics.
The effect of a spherical monodromy defect on the entanglement entropy and central charge $C_T$ of a free conformal scalar field propagating on an odd-dimensional sphere is investigated. As on even spheres the central charge becomes negative for a range of the flux parameter, $δ$, with possible implications for reflection positivity. The work is mostly numerical but closed forms are found for the $Z_2$ monodromy ($δ=1/2$) yielding an explicit $d\to\infty$ limit, $C_T\to -6/π$
p-Balls are topological defects in $(D,1)$ dimensions constructed with $\mathcal{M}\ge 1$ scalar fields which depend radially on only $2 \le p\le D-2$ spatial dimensions. Such defects are characterized by an action that breaks translational invariance and are inspired on the physics of a brane with $D-p$ extra dimensions. Here we consider the issue of localization of bosonic states described by a scalar field $Φ$ sufficiently weak to not disturb sensibly the defect configuration. After describing the general formalism, we consider some specify examples with $\mathcal{M}=1,2$ and $3$, looking f…
An algebraic framework for quantization in presence of arbitrary number of point-like defects on the line is developed. We consider a scalar field which interacts with the defects and freely propagates away of them. As an application we compute the Casimir force both at zero and finite temperature. We derive also the charge density in the Gibbs state of a complex scalar field with defects. The example of two delta-defects is treated in detail.
We study the diffusion processes of a real scalar field in the presence of the distorsion field induced by a chiral topological defect. The defect modifies the usual Euclidean background geometry into a non-diagonal Riemann-Cartan geometry characterized by a singular torsion field. The new form of the diffusion equation is established and the scalar field distribution in the vicinity of the defect is investigated numerically. Results show a high sensitivity to the boundary conditions. In the transient regime, we find that the defect vorticity generates an angular momentum associated to the dif…
We consider Lagrangians in 3+1 dimensions admitting topological defects where there is an additional coupling between the defect scalar field $Φ$ and the gauge field kinetic term (eg $B(\vert Φ\vert^2) F_{μν}F^{μν}$). Such a {\it dilatonic} coupling in the context of a static defect, induces a spatially dependent effective gauge charge and effective mass for the scalar field which leads to modified properties of the defect core. In particular, the scale of the core gets modified while the stability properties of the corresponding embedded defects are also affected. These modifications are illu…
