Quark zero modes in intersecting center vortex gauge fields

Abstract

The zero modes of the Dirac operator in the background of center vortex gauge field configurations in ${\mathbb{R}}^2$ and ${\mathbb{R}}^4$ are examined. If the net flux in D=2 is larger than 1 we obtain normalizable zero modes which are mainly localized at the vortices. In D=4 quasi-normalizable zero modes exist for intersecting flat vortex sheets with the Pontryagin index equal to 2. These zero modes are mainly localized at the vortex intersection points, which carry a topological charge of $\pm 1/2$. To circumvent the problem of normalizability the space-time manifold is chosen to be the (compact) torus $\T^2$ and $\T^4$, respectively. According to the index theorem there are normalizable zero modes on $\T^2$ if the net flux is non-zero. These zero modes are localized at the vortices. On $\T^4$ zero modes exist for a non-vanishing Pontryagin index. As in ${\mathbb{R}}^4$ these zero modes are localized at the vortex intersection points.

20 pages, 4 figures, LaTeX2e, references added, treatment of ideal vortices on the torus shortened

References in corpus (3)

• Topology of Center Vortices
• Constituents of Doubly Periodic Instantons
• Confinement and Chiral Symmetry

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