Spectral flow of the Dirac spectrum in intersecting vortices
arXiv:hep-th/0302100 · doi:10.1103/PhysRevD.68.065004
Abstract
The spectrum of the Dirac Hamiltonian in the background of crossing vortices is studied. To exploit the index theorem, and in analogy to the lattice the space-time manifold is chosen to be the four-torus $\T^4$. For sake of simplicity we consider two idealized cases: infinitely fat and thin transversally intersecting vortices. The time-dependent spectrum of the Dirac Hamiltonian is calculated and in particular the influence of the vortex crossing on the quark spectrum is investigated. For the infinitely fat intersecting vortices it is found that zero modes of the four-dimensional Dirac operator can be expressed in terms of those eigenspinors of the Euclidean time-dependent Dirac Hamiltonian, which cross zero energy. For thin intersecting vortices the time gradient of the spectral flow of the Dirac Hamiltonian is steepest at the time at which the vortices cross each other.
arXiv comment19 pages, 11 figures, references added, minor corrections
References in corpus (16)
- The Confinement Problem in Lattice Gauge Theory
- Center Dominance and Z2 Vortices in SU(2) Lattice Gauge Theory
- On the relevance of center vortices to QCD
- Deconfinement in SU(2) Yang-Mills theory as a center vortex percolation transition
- Center Projection Vortices in Continuum Yang-Mills Theory
- Center vortex model for the infrared sector of Yang-Mills theory - Confinement and Deconfinement
- Topology of Center Vortices
- Computation of the Vortex Free Energy in SU(2) Gauge Theory
- Quark zero modes in intersecting center vortex gauge fields
- Center Vortices, Nexuses, and Fractional Topological Charge
- Chiral symmetry restoration and the Z3 sectors of QCD
- Spectral flow of chiral fermions in nondissipative Yang-Mills gauge field backgrounds
- Fermion Number Violation in the Background of a Gauge Field in Minkowski Space
- Deconfinement and Chiral Symmetry Restoration
- Center vortex model for the infrared sector of Yang-Mills theory
- Center vortex model for the infrared sector of Yang-Mills theory