Quark zero modes in intersecting center vortex gauge fields

H. Reinhardt, O. Schröder, T. Tok, and V. Ch. Zhukovsky
Phys. Rev. D 66, 085004 – Published 11 October 2002
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Abstract

The zero modes of the Dirac operator in the background of center vortex gauge field configurations in R2 and R4 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 quasinormalizable 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 ±12. To circumvent the problem of normalizability the space-time manifold is chosen to be the (compact) torus T2 and T4, respectively. According to the index theorem there are normalizable zero modes on T2 if the net flux is nonzero. These zero modes are localized at the vortices. On T4 zero modes exist for a nonvanishing Pontryagin index. As in R4 these zero modes are localized at the vortex intersection points.

  • Received 26 March 2002

DOI:https://doi.org/10.1103/PhysRevD.66.085004

©2002 American Physical Society

Authors & Affiliations

H. Reinhardt, O. Schröder, and T. Tok

  • University of Tübingen, D-72076 Tübingen, Germany

V. Ch. Zhukovsky

  • Moscow State University, Moscow, Russia

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Issue

Vol. 66, Iss. 8 — 15 October 2002

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