Related papers: Chiral structures on the 4D spin cobordism categor…
Second-order equations of motion on a group manifold that appear in a large class of so-called chiral theories are presented. These equations are presented and explicitely solved for cases of semi-simple, finite-dimensional Lie groups. With…
In this article we construct and discuss several aspects of the two-component spinorial formalism for six-dimensional spacetimes, in which chiral spinors are represented by objects with two quaternionic components and the spin group is…
This is a short review of the papers arXiv:1109.2904 and arXiv:1110.4639. After a reminder about local and global gravitational anomalies, we sketch the derivation of the global gravitational anomaly of the self-dual field theory (also…
The results of this paper are outdated. Finer versions of them will appear elsewhere.
Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R^4 can be described as certain 2-morphisms in the 2-category of `2-tangles in 4…
We experimentally investigate the chiral optical response of an individual nanostructure consisting of three equally sized spherical nanoparticles made of different materials and arranged in \ang{90} bent geometry. Placing the nanostructure…
The set of one dimensional lowest energy eigenspaces used to construct the overlap induces a two form on gauge orbit space which is the locally exact curl of Berry's connection. If anomalies do not cancel, examples of two dimensional closed…
Some aspects of chiral p-forms, in particular the obstruction that makes it hard to define covariant Green functions, are discussed. It is shown that a proposed resolution involving an infinite set of gauge fields can be made mathematically…
This is the second in a series of papers on a new equivariant cohomology that takes values in a vertex algebra. In an earlier paper, the first two authors gave a construction of the cohomology functor on the category of O(sg) algebras. The…
We review the theory of higher-spin gauge fields in four and three space-time dimensions and present some new results on higher-spin gauge interactions of matter fields in two dimensions.
Chiral spin textures such as skyrmions have attracted considerable attention due to their nontrivial topology, chirality, stability at the nanoscale, and potential for low-power spintronic devices. The recent discovery of intrinsic…
This paper presents a technique for constructing new chiral or regular polyhedra (or maps) from self-dual abstract chiral polytopes of rank 4. From improperly self-dual chiral polytopes we derive "Petrie-Coxeter-type" polyhedra (abstract…
We present a comparison of various five-dimensional representations of chiral fermions considering their cost and residual chiral symmetry breaking.
We present a comprehensive overview of chirality and its optical manifestation in plasmonic nanosystems and nanostructures. We discuss top-down fabricated structures that range from solid metallic nanostructures to groupings of metallic…
The recent progress of multiple chiral doublet bands (M$\chi$D) is reviewed for both experimental and theoretical sides. In particular, the experimental findings, theoretical predictions, selection rule for electromagnetic transitions,…
Chirality refers to a geometric phenomenon in which objects are not superimposable on their mirror image. Structures made of nano-scale chiral elements can display chiroptical effects, such as dichroism for left- and right- handed…
We consider low-$x$ behavior of the spin structure functions $g_1(x)$ and $h_1(x)$ in the unitarized chiral quark model that combines the ideas on constituent quark structure of hadrons with a geometrical scattering picture and unitarity. A…
Cobordism of virtual string links on $n$ strands is a combinatorial generalization of link cobordism. There exists a bijection between virtual string links up to cobordisms and elements of the group $\mathbb{Z}^{n(n-1)}$. This paper also…
Inspired by Lurie's theory of quasi-unital algebras we prove an analogous result for $\infty$-categories. In particular, we show that the unital structure of an $\infty$-category can be uniquely recovered from the underlying non-unital…
The parameter-space orbifold construction of open and unoriented toroidal and (target-space) orbifold compactifications is briefly reviewed, with emphasis on the underlying geometrical framework. A class of chiral four-dimensional type-I…