Spectral flow of the Dirac spectrum in intersecting vortices

Details Spectral flow of the Dirac spectrum in intersecting vortices Spectral flow of the Dirac spectrum in intersecting vortices

2003-02-13

arxiv.org/abs/hep-th/0302100v2

Phys.Rev. D68 (2003) 065004

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, 11 figures, references added, minor corrections

Scientific paper

10.1103/PhysRevD.68.065004

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.

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