Related papers: A geometric view of the Chern character
We present a new, alternative interpretation of the vector-tensor multiplet as a 2-form in central charge superspace. This approach provides a geometric description of the (non-trivial) central charge transformations ab initio and is…
As a generalisation of the correspondence linking 2D integrable systems with 4D Chern-Simons (CS) gauge theory, superspin chains are realized by means of crossing electric and magnetic super line defects in the 4D CS with super gauge…
Some cohomology elements, called $\nu$ classes, as a supergeneralization of universal Chern classes, are introduced for canonical super line bundles over $\nu$ projective spaces, a novel supergeometric generalization of projective spaces.…
In this work we will explore the properties of superconducting surfaces decorated by two-dimensional ferromagnetic adatom lattices. As discovered recently [R\"ontynen and Ojanen, Phys. Rev. Lett. \textbf{114}, 236803 (2015)], in the…
This paper considers a hyperplane arrangement constructed with a subset of a set of all simple paths in a graph. A connection of the constructed arrangement to the maximum matching problem is established. Moreover, the problem of finding…
We study anomalies of fermions with spacetime dependent mass. Using Fujikawa's method, it is found that the anomalies associated with the $U(N)_+\times U(N)_-$ chiral symmetry and $U(N)$ flavor symmetry for even and odd dimensions,…
In this note we define Chern-Simons classes of a superconnection $D+L$ on a complex supervector bundle $E$ such that $D$ is flat and preserves the grading, and $L$ is an odd endomorphism of $E$ on a supermanifold. As an application we…
We relate a generic character sheaf on a disconnected reductive group with a character of a representation of the rational points of the group over a finite field extending a result known in the connected case.
In this short note we give an elementary proof of the fact that connections and their geometric parallel-transport counterpart are equivalent notions.
The aim of this note is to improve upon our earlier result which translates Weyl's (curvature) formulation of Chern character of a smooth vector bundle into the language of residues. The dualized Chern character is the functional on smooth…
The off-shell vector-tensor multiplet is considered in an arbitrary background of N=2 vector supermultiplets. We establish the existence of two inequivalent versions, characterized by different Chern-Simons couplings. In one version the…
General expressions are given for the coefficients of Chern forms up to the 13th order in curvature in terms of the Riemann-Christoffel curvature tensor and some of its concomitants (e.g., Pontrjagin's characteristic tensors) for…
Three dimensional SU(2) Chern-Simons theory has been studied as a topological field theory to provide a field theoretic description of knots and links in three dimensions. A systematic method has been developed to obtain the link-invariants…
We study observables and deformations of generalized Chern-Simons action and show how to apply these results to maximally supersymmetric gauge theories. We describe a construction of large class of deformations based on some results on the…
We study coherent quantum transport through a superconducting film connected to normal-metal electrodes. Simple expressions for the differential conductance and the local density of states are obtained in the clean limit and for transparent…
We express supersymmetric couplings among the vector and the tensor multiplets in six dimensions (6D) in terms of N=1 superfields. The superfield description is derived from the invariant action in the projective superspace. The obtained…
We derive the equations of chains for path geometries on surfaces by solving the equivalence problem of a related structure: sub-Riemannian geometry of signature $(1,1)$ on a contact 3-manifold. This approach is significantly simpler than…
Motivated by the geometric character of spin Hall conductance, the topological invariants of generic superconductivity are discussed based on the Bogoliuvov-de Gennes equation on lattices. They are given by the Chern numbers of degenerate…
We study the sub-gap spectrum and the transport properties of a double quantum dot coupled to metallic and superconducting leads. The coupling of both quantum dots to the superconducting lead induces a non-local pairing in both quantum dots…
Using the theory of quantized equivariant vector bundles over compact coadjoint orbits we determine the Chern characters of all noncommutative line bundles over the fuzzy sphere with regard to its derivation based differential calculus. The…