Related papers: On the non-existence of zero modes
A novel feature of a Ginsparg-Wilson lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this lattice Dirac operator does not possess topological zero modes for any topologically-nontrivial…
This paper is devoted to the study of the spectral properties of the Weyl-Dirac or massless Dirac operators, describing the behavior of quantum quasi-particles in dimension 2 in a homogeneous magnetic field, $B^{\rm ext}$, perturbed by a…
We use geometric arguments to derive a possible form for the radial part of the ``zero-mode Hamiltonian'' for the two dimensional sigma model with target space S^3, or more generally a compact simply connected Lie group.
We study fermionic zero modes in the domain wall background. The fermions have Dirac and left- and right-handed Majorana mass terms. The source of the Dirac mass term is the coupling to a scalar field $\Phi$. The source of the Majorana mass…
Constructing an effective field theory in terms of doped magnetic impurities (described by an O(3) vector model with a random mass term), itinerant electrons of spin-orbit coupled semiconductors (given by a Dirac theory with a relatively…
We give estimates for the eigenvalues of multi-form modified Dirac operators which are constructed from a standard Dirac operator with the addition of a Clifford algebra element associated to a multi-degree form. In particular such…
The tetragonal ferrimagnetic Mn$_3$Ga exhibits a wide range of intriguing magnetic properties. Here, we report the emergence of topologically nontrivial nodal lines in the absence of spin orbit coupling (SOC) which are protected by both…
The Dirac equation with a U(1) vortex in the mass-term is solved in the presence of magnetic-like fields at zero energy. By drawing an analogy to classical mechanics, it is shown that the four-component Dirac equation in arbitrary magnetic…
Stationary and axially symmetric space-times play an important role in astrophysics, particularly in the theory of neutron stars and black holes. The static vacuum sub-class of these space-times is known as Weyl's class, and contains the…
A recent experiment on Nb-doped Bi2Se3 showed that zero field magnetization appears below the superconducting transition temperature. This gives evidence that the superconducting state breaks time-reversal symmetry spontaneously and…
Energy momentum tensors of higher-derivative free scalar conformal field theories in flat spacetime are discussed. Two algorithms for the computation of energy momentum tensors are described, which accomplish different goals: the first is…
The connected components of the zero set of any conformal vector field, in a pseudo-Riemannian manifold of arbitrary signature, are shown to be totally umbilical conifold varieties, that is, smooth submanifolds except possibly for some…
Dirac metals (gapless semi-conductors) are believed to turn into Weyl metals when perturbations, which break either time reversal symmetry or inversion symmetry, are employed. However, no experimental evidence has been reported for the…
Normal modes, quasi-normal modes and super-radiant modes are studied to clarify the total dynamics for complex scalar fields in Kerr anti-de Sitter black hole spacetime. Orthonormal relations and quasi-orthonormal relations are obtained for…
We study zero modes of Laplacians on compact and non-compact metric graphs with general self-adjoint vertex conditions. In the first part of the paper the number of zero modes is expressed in terms of the trace of a unitary matrix…
Dirac's formulation of magnetic monopoles is shown to be equivalent to Maxwell theory coupled to 2-form gauge fields so that it has a local 1-form symmetry, with the 2-form gauge fields given in terms of the 2-form current densities…
The motion of massless particles on the background of a toroidal topological black hole is analyzed in the context of conformal Weyl gravity. Null geodesics, in terms of the Jacobi elliptic functions, are found analytically. In addition,…
We present a novel perspective to characterize the chiral magnetic and related effects in terms of angular decomposed modes. We find that the vector current and the chirality density are connected through a surprisingly simple relation for…
We study topological aspects of the QCD vacuum structure in SU(2) lattice gauge theory with the abelian gauge fixing. The index of the Dirac operator is measured by using the Wilson fermion in the quenched approximation. We find…
Owing to the chirality of Weyl nodes characterized by the first Chern number, a Weyl system supports one-way chiral zero modes under a magnetic field, which underlies the celebrated chiral anomaly. As a generalization of Weyl nodes from…