Related papers: Defect Structures in Field Theory
In the first part of the paper we define a perturbative (pre-formal) geometry and formulate a theorem on the relation between the construction of a perturbative neighborhood of affine varieties and the higher tangent bundles. In the second…
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
The problem of extending fields that are defined on lattices to fields defined on the continua that they become in the continuum limit is basically one of continuous extension from the 0-skeleton of a simplicial complex to its…
This paper deals with properties of the algebraic variety defined as the set of zeros of a "deficient" sequence of multivariate polynomials. We consider two types of varieties: ideal-theoretic complete intersections and absolutely…
The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase…
This is a non-standard paper, containing some problems, mainly in model theory, which I have, in various degrees, been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me,…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
We investigate defects in scalar field theories in four and six dimensions in a double-scaling (semiclassical) limit, where bulk loops are suppressed and quantum effects come from the defect coupling. We compute $\beta $-functions up to…
This is a lecture note prepared for the SFT 9 workshop in Augsburg, Germany. The text describes a polyfold approach to the construction of symplectic field theory and focuses on the perturbation and transversality theory.
At the present work we consider an application of the deformation procedure that enable us to construct, systematically, scalar field models supporting multikinks. We introduce a new deformation function in order to realize this task. We…
We construct field theories in $2+1$ dimensions with multiple conformal symmetries acting on only one of the spatial directions. These can be considered a conformal extension to "subsystem scale invariances", borrowing the language often…
In this work we investigate the presence of defect structures in models described by two real scalar fields. The coupling between the two fields is inspired on the equations for a multimode laser, and the minimum energy trivial…
We review the interplay of fuzzy field theories and matrix models, with an emphasis on the phase structure of fuzzy scalar field theories. We give a self-contained introduction to these topics and give the details concerning the saddle…
A supersymmetric theory with several scalar superfields generically has several domain wall type classical configurations which interpolate between various supersymmetric vacua of the scalar fields. Depending on the couplings, some of these…
We introduce a field theoretic formalism enabling the direct study of dislocation and interstitial dynamics. Explicit expressions for the energies of such defects are given. We provide links to earlier numerical, discrete elastic, time…
Topological defects, in particular cosmic strings, give rise to an interesting mechanism for generating the primordial perturbations in the early Universe which are required to explain the present structure. An overview of the cosmic string…
The divergences coming from a particular sector of gravitational fluctuations around a generic background in general theories of quadratic gravity are analyzed. They can be summarized in a particular type of scalar model, whose properties…
We give an introduction to the structure theory of extended affine Lie algebras, which provide a common framework for finite-dimensional semisimple, affine and toroidal Lie algebras. The notes are based on a lecture series given during the…
We deal with the presence of topological defects in models for two real scalar fields. We comment on defects hosting topological defects, and we search for explicit defect solutions using the trial orbit method. As we know, under certain…
In this work we study models described by a single real scalar field in two-dimensional space-time, using the deformation procedure to propose and investigate new families of models and their kink solutions.