Related papers: Defects in affine Toda field theories
A model of soliton-defect interactions in the sine-Gordon equations is studied using singular perturbation theory. Melnikov theory is used to derive a critical velocity for strong interactions, which is shown to be exponentially small for…
It is shown that the $n$-dimensional Jacobian conjecture over algebraic number fields may be considered as an existence problem of integral points on affine curves. More specially, if the Jacobian conjecture over $\mathbb{C}$ is false, then…
There are two prominent applications of the mathematical concept of topology to the physics of materials: band topology, which classifies different topological insulators and semimetals, and topological defects that represent immutable…
We discuss topological theories, arising from the general $\mathcal{N}=2$ twisted gauge theories. We initiate a program of their study in the Gromov-Witten paradigm. We re-examine the low-energy effective abelian theory in the presence of…
We study the structure of superselection sectors of an arbitrary perturbation of a conformal field theory. We describe how a restriction of the q-deformed $\hat{sl(2)}$ affine Lie algebra symmetry of the sine-Gordon theory can be used to…
Conceptual difficulties in semiclassical and quantum gravity arise from diffeomorphism invariance of classical general relativity. With a motivation to shed some light on these difficulties, we study a class of toy models for which…
Affine Toda field theories in two dimensions constitute families of integrable, relativistically invariant field theories in correspondence with the affine Kac-Moody algebras. The particles which are the quantum excitations of the fields…
The language and methods of algebraic topology, particularly homotopy theory, have been extensively used in the study of the identification, the classification and the evolution of defects. Topological methods provide the means for the…
We study different aspects of integrable boundary quantum field theories, focusing mostly on the ``boundary sine-Gordon model'' and its applications to condensed matter physics. The first part of the review deals with formal problems. We…
We argue that topological compactons (solitons with compact support) may be quite common objects if $k$-fields, i.e., fields with nonstandard kinetic term, are considered, by showing that even for models with well-behaved potentials the…
1+1 dimensional integrable quantum field theories correspond to a sparse subset of quantum field theories where the calculation of physically interesting observables can be brought to explicit, closed and manageable expressions thanks to…
This paper is the first in a series where we attempt to define defects in critical lattice models that give rise to conformal field theory topological defects in the continuum limit. We focus mostly on models based on the Temperley-Lieb…
In this paper we investigate in more detail our previous formulation of the dilaton-gravity theory by Bilal--Callan--de~Alwis as a $SL_2$-conformal affine Toda (CAT) theory. Our main results are: i) a field redefinition of the CAT-basis in…
Defects which appear in heterostructure junctions involving topological insulators are sources of gapless modes governing the low energy properties of the systems, as recently elucidated by Teo and Kane [Physical Review B82, 115120 (2010)].…
We discuss Born-Infeld type fields (tachyon fields) in classical and quantum cosmology. We first partly review and partly extend the discussion of the classical solutions and focus in particular on the occurrence of singularities. For…
This work deals with defect structures in models described by scalar fields. The investigations focus on generalized models, with the kinetic term modified to allow for a diversity of possibilities. We develop a new framework, in which we…
It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as…
We investigate quantum integrals of motion in the sine-Gordon, Zhiber-Shabat and similar systems. When the coupling constants in these models take special values a new quantum symmetry appears. In those cases, correlation functions can be…
We study the Toda field theory with finite Lie algebras using an extension of the Goulian-Li technique. In this way, we show that, after integrating over the zero mode in the correlation functions of the exponential fields, the resulting…
Two different conformal field theories can be joined together along a defect line. We study such defects for the case where the conformal field theories on either side are single free bosons compactified on a circle. We concentrate on…