相关论文: Cohomology and Topological Anomalies

A geometrical interpretation of the consistent and covariant chiral anomaly is done in the space-time respective Hamiltonian framework.

By completing the old discussion of K.~Wilson, we express the chiral anomaly in terms of a double integral of a three-point function of chiral currents over an arbitrarily small region in the coordinate space. An integrability condition…

We discuss the noncommutative counterparts of chiral gauge theories and compute the associated anomalies.

We consider chiral gauge theories defined over a four-dimensional spacetime manifold with a Cartesian product structure for at least one compact spatial dimension. For a simple setup, we calculate the effective gauge field action by…

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…

When a quantum field theory has a symmetry, global or local like in gauge theories, in the tree or classical approximation formal manipulations lead to believe that the symmetry can also be implemented in the full quantum theory, provided…

Using cohomological methods we discuss several issues related to chiral anomalies in noncommutative U(N) YM theories in any even dimension. We show that for each dimension there is only one solution of the WZ consistency condition and that…

Topology, a well-established concept in mathematics, has nowadays become essential to describe condensed matter. At its core are chiral electron states on the bulk, surfaces and edges of the condensed matter systems, in which spin and…

The chiral equivariant cohomology contains and generalizes the classical equivariant cohomology of a manifold M with an action of a compact Lie group G. For any simple G, there exist compact manifolds with the same classical equivariant…

General features of microscopic and macroscopic chiral structures can be discussed under the standard of orthogonal group theory. Configuration space of systems, not physical space, is taken into account. This change of perspective allows…

We investigate chiral anomaly for fermions in fundamental representation on noncommutative (fuzzy) 2-sphere. In spite that this system is realized by finite dimensional matrices and no regularization is necessary for either UV or IR, we can…

We reproduce the quantum cohomology of toric varieties (and of some hypersurfaces in projective spaces) as the cohomology of certain vertex algebras with differential. The deformation technique allows us to compute the cohomology of the…

A calculation of the chiral anomaly on a finite lattice without fermion doubling is presented . The lattice gauge field is defined in the spirit of noncommutative geometry. Standard formulas for the continuum anomaly are obtained as a…

The chiral anomaly is based on a non-conserved chiral charge and can happen in Dirac fermion systems under the influence of external electromagnetic fields. In this case, the spectral flow leads to a transfer of right- to left-moving…

Chiral defect fermions in the background of an external, $2n$ dimensional gauge field are considered. Assuming first a finite extra dimension, we calculate the axial anomaly in a vector-like, gauge invariant model for arbitrary $n$, and the…

We define chiral fermions in the presence of non-trivial gravitational and gauge background fields in the framework of locally covariant field theory. This allows to straightforwardly compute the chiral anomalies on non-compact Lorentzian…

It is pointed out that the chiral anomaly in 1+1 dimensions should be observed in toroidal carbon nanotubes on a planar geometry with varying magnetic field. We show that the chiral anomaly is closely connected with the persistent current…

Dirac fermions coupled to gauge fields can exhibit the chiral anomaly even on a finite spatial lattice. A careful description of this phenomenon yields new insights into the nature of spin-charge relations and on-site symmetries (symmetries…

Anomalies can be viewed as arising from the cohomology of the Lie algebra of the group of gauge transformations and also from the topological cohomology of the group of connections modulo gauge transformations. We show how these two…

We revisit the relation between black hole geometries and chiral transport. Integrating the anomaly equation in a black hole geometry allows to derive the chiral transport coefficients for the thermal gas far from the horizon. The key…