相关论文: Kink Chains from Instantons on a Torus

There are several knot invariants in the literature that are defined using singular instantons. Such invariants provide strong tools to study the knot group and give topological applications. For instance, it gives powerful tools to study…

We describe how an approximation to the minimal energy Skyrme crystal can be obtained from the holonomy of a Yang-Mills instanton. The appropriate instanton is twisted on a four-torus and has instanton number equal to one half. It generates…

We consider cones over manifolds admitting real Killing spinors and instanton equations on connections on vector bundles over these manifolds. Such cones are manifolds with special (reduced) holonomy. We generalize the scalar ansatz for a…

The holonomy of an SU(2) N-instanton in the x^4-direction gives a map from R^3 into SU(2), which provides a good model of an N-Skyrmion. Combining this map with the standard Hopf map from SU(2)=S^3 to S^2 gives a configuration for a Hopf…

Concordance invariants of knots are derived from the instanton homology groups with local coefficients, as introduced in earlier work of the authors. These concordance invariants include a 1-parameter family of homomorphisms $f_{r}$, from…

We investigate propagation of a kink soliton along inhomogeneous chains with two different constituents, arranged either periodically, aperiodically, or randomly. For the discrete sine-Gordon equation and the Fibonacci and Thue-Morse chains…

Kronheimer and Mrowka asked whether the difference between the four-dimensional clasp number and the slice genus can be arbitrarily large. This question is answered affirmatively by studying a knot invariant derived from equivariant…

Atiyah and Manton have outlined a scheme to obtain approximations to the SU(2) skyrmions from instantons in $\R^4$. In this paper we apply this scheme to construct, in an explicit form, approximations to static spherically symmetric SU(N)…

A spectral sequence is established, from Bar-Natan's variant of Khovanov homology to a deformation of instanton homology for knots and links. This spectral sequence arises as a specialization of a spectral sequence from a characteristic-2…

We study discrete solitons (kinks) accessible in state-of-the-art trapped ion experiments, considering zigzag crystals and quasi-3D configurations, both theoretically and experimentally. We first extend the theoretical understanding of…

Some time ago, Atiyah and Manton observed that computing the holonomy of Yang-Mills instantons yields good approximations to static Skyrmion solutions of the Skyrme model. This paper provides an extension and explanation of this result, by…

The cross section for scattering of x-rays by solitons is calculated. The authors consider solitons corresponding to the formation of a kink in a system of adatoms on the surface of a substrate, or of a crowdion in a chain of atoms in a…

We establish the duality between the torus knot superpolynomials or the Poincar\'e polynomials of the Khovanov homology and particular condensates in $\Omega$-deformed 5D supersymmetric QED compactified on a circle with 5d Chern-Simons(CS)…

We present the idea of using the holonomy along a line of a constrained instanton solution (an approximate solution of the Euclidean equations of motion subject to a constraint) of an $\rm SU(2)$ Yang-Mills-Higgs theory to approximate the…

We construct a modified non-BPS sine-Gordon theory which supports stable static kinks of arbitrary topological degree $N$. We use this toy model to study problems which are interesting for higher-dimensional soliton theories supporting…

Lattice artefacts are used, through modified lattice actions, as a tool to find the largest instantons in a toroidal geometry [0,L]^3X[0,T] for T to infinity. It is conjectured that the largest instanton is associated with tunnelling…

Knotted fields in classical and quantum systems have long been recognized for their non-trivial topologies and particle-like behavior, but practical applications have been limited by the difficulty of stabilizing them. Recently, stable…

The aim of this paper is to realise the techniques of picture-valued invariants and invariants valued in free groups for long knots in the full torus. Such knots and links are of a particular interest because of their relation to Legendrian…

We prove the existence of an infinite number of internal (shape) modes of sine-Gordon solitons in the presence of some inhomogeneous long-range forces, provided some conditions are satisfied.

We describe a one-dimensional kink crystal, which represents a collection of equal and equally localized kinks forming a lattice in the real axis. The results are analytical, original and may motivate other studies on localized structures…