Related papers: On the domain of moduli fields
We show that if A is an abelian category satisfying certain mild conditions, then one can introduce the concept of a moduli space of (semi)stable objects which has the structure of a projective algebraic variety. This idea is applied to…
A general approach allowing to find the analytical expressions for equilibrium magnetic structures in small and flat magnetic nano-sized cylinders of arbitrary shape made of soft magnetic material is presented. The resulting magnetization…
We study formation and evolution of solitons within a model with two real scalar fields with the potential having a saddle point. The set of these configurations can be split into disjoint equivalence classes. We give a simple expression…
We review our recent works on solitons in U(Nc) gauge theories with Nf (>Nc) Higgs fields in the fundamental representation, which possess eight supercharges. The moduli matrix is proposed as a crucial tool to exhaust all BPS solutions, and…
We describe the topology of the moduli spaces of flat metrics for all the 3-dimensional closed manifolds. We give an algebraic description of the moduli spaces for the 4-dimensional closed flat manifolds with a single generator in their…
A scenario which overcomes the well-known cosmological overshoot problem associated with stabilizing moduli with steep potentials in string theory is proposed. Our proposal relies on the fact that moduli potentials are very steep and that…
We investigate moduli field dynamics in supergravity/M-theory like set ups where we turn on fluxes along some or all of the extra dimensions. As has been argued in the context of string theory, we observe that the fluxes tend to stabilize…
Brane models at low energy are described by an effective action involving gravity and two moduli fields associated with the brane positions. The scalar-tensor nature of the effective theory and the coupling to matter are explicitly spelt…
Magnetic solitons offer functionalities as information carriers in multiple spintronic and magnonic applications. However, their potential for nanoscale energy transport has not been revealed. Here we demonstrate that antiferromagnetic…
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…
Solitons are self-sustained wavepackets that occur in many physical systems. Their recent demonstration in optical microresonators has provided a new platform for study of nonlinear optical physics with practical implications for…
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…
We present a simple laboratory experiment to illustrate some aspects of the soliton theory in discrete lattices with a system that models the dynamics of dislocations in a crystal or the properties of adsorbed atomic layers. The apparatus…
A general approach allowing to construct the magnetization distributions of arbitrary topological charge in small exchange-dominated cylindrical ferromagnetic particles is presented. The exchange energy functional is minimized by these…
We consider an hierarchy of integrable 1+2-dimensional equations related to Lie algebra of the vector fields on the line. The solutions in quadratures are constructed depending on $n$ arbitrary functions of one argument. The most…
In this paper, continuing the discussion about Species Quantum Mechanics, we investigate quantum mechanics in moduli spaces using a mini-superspace approach. From this perspective, moduli-dependent functions can be viewed as operators, and…
We present an application of the basic mathematical concept of complex functions as topological solitons, a most interesting area of research in physics. Such application of complex theory is virtually unknown outside the community of…
Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…
A scalar field theory is constructed on an energy-momentum background of constant curvature. The generalization of the usual Feynamn rules for the flat geometry follows from the requirement of their covariance. The main result is that the…
Continuous cellular automata are rocketing in popularity, yet developing a theoretical understanding of their behaviour remains a challenge. In the case of Lenia, a few fundamental open problems include determining what exactly constitutes…