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The present paper introduces the concept of monotone Hopf-harmonics in $2D$ as an alternative to harmonic homeomorphisms. It opens a new area of study in Geometric Function Theory (GFT). Much of the foregoing is motivated by the principle…
We report the discovered class of exact static solutions of several 4D Einstein-Maxwell-dilaton systems: string-induced, Liouville, trigonometric, polynomial, etc., for three basic topologies (spherical, hyperbolical and flat) being…
Quantum field theories on noncommutative Minkowski space are studied in a model-independent setting by treating the noncommutativity as a deformation of quantum field theories on commutative space. Starting from an arbitrary Wightman…
In mimetic gravity, we derive $D$-dimension charged black hole solutions having flat or cylindrical horizons with zero curvature boundary. The asymptotic behaviours of these black holes behave as (A)dS. We study both linear and nonlinear…
Knots are fascinating topological structures that have been observed in various contexts, ranging from micro-worlds to macro-systems, and are conjectured to play a fundamental role in their respective fields. In order to characterize their…
We consider topological structure of classical vacuum solutions in quantum chromodynamics. Topologically non-equivalent vacuum configurations are classified by non-trivial second and third homotopy groups for coset of the color group SU(N)…
We clarify the relation between noncommutative spacetimes and multifractional geometries, two quantum-gravity-related approaches where the fundamental description of spacetime is not given by a classical smooth geometry. Despite their…
Tight bosonic analogs of free-fermionic symmetry-protected topological phases, and their associated edge-localized excitations, have long evaded the grasp of condensed-matter and AMO physics. In this work, building on our initial…
Conformal electrodynamics is a particularly interesting example of power Maxwell non-linear electrodynamics, designed to possess conformal symmetry in all dimensions. In this paper, we propose a regularized version of Conformal…
Recently, much research has been dedicated to understanding topological superconductivity and Majorana zero modes induced by a magnetic field in hybrid proximity structures. This paper proposes a realization of topological superconductivity…
We have studied numerically Faddeev-Hopf knots, which are defined as those unit-vector fields in $R^3$ that have a nontrivial Hopf charge and minimize Faddeev's Lagrangian. A given initial configuration was allowed to relax into a (local)…
The complete classification of classical $r$-matrices generating quantum deformations of the (3+1)-dimensional (A)dS and Poincar\'e groups such that their Lorentz sector is a quantum subgroup is presented. It is found that there exists…
Recently there had been a great deal of activity associated with various schemes of designing both analytical and experimental methods describing knotted structures in electrodynamics and in hydrodynamics.The majority of works in…
The discrete static properties of a class of deformable double-well potential models are investigated. The Peierls-stress potential of the models is explicitely given. Numerical analysis of the equation of motion reveal different soliton…
In this paper, we consider the Reshetikhin-Turaev invariants of knots in the three-sphere obtained from a twisted Drinfeld double of a Hopf algebra, or equivalently, the relative Drinfeld center of the crossed product…
Motivated by experiments in electroconvection in nematic liquid crystals with homeotropic alignment we study the coupled amplitude equations describing the formation of a stationary roll pattern in the presence of a weakly-damped mode that…
We study novel conformal twist defects in 4d Maxwell theory, around which electric and magnetic fields are exchanged. These are codimension-2 defects living at the end of topological defects for certain non-invertible global symmetries. We…
We investigate the properties of kappa-Minkowski spacetime by using representations of the corresponding deformed algebra in terms of undeformed Heisenberg-Weyl algebra. The deformed algebra consists of kappa-Poincare algebra extended with…
We consider a four-dimensional N=2 gauged supergravity coupled to matter fields. The model is obtained by a U(1) gauging of a charged hypermultiplet and therefore it is suitable for the study of holographic superconductivity. The potential…
The defect-type solutions of a deformed $O(2N+1)$ linear sigma model with a real and $N$ complex fields in $(1+1)$-dimensional Minkowski spacetime are studied. All the solutions are analytically found for the $N=2$ case. Two types of…