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Yukawa coupling in three dimensions

Physical Review D - Particles, Fields, Gravitation and Cosmology, ISSN: 1550-2368, Vol: 57, Issue: 2, Page: 1159-1166
1998
  • 10
    Citations
  • 0
    Usage
  • 3
    Captures
  • 0
    Mentions
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Metrics Details

  • Citations
    10
    • Citation Indexes
      10
  • Captures
    3

Article Description

We consider several renormalizable, scale free models in three space-time dimensions which involve scalar and spinor fields. The Yukawa couplings are bilinear in both the spinor and scalar fields and the potential is of sixth order in the scalar field. In a model with a single scalar field and a complex fermion field in three Euclidean dimensions, the couplings in the theory are both asymptotically free. This property is not retained in (Formula presented)-dimensional Minkowski space, as we illustrate by considering a renormalizable scale-free supersymmetric model. This is on account of the different properties of the Dirac matrices in Euclidean and Minkowski space. We also examine a model in (Formula presented)-dimensional Minkowski space in which two species of fermions, associated with the two unitarily inequivalent representations of the (Formula presented) Dirac matrices, couple in two different ways to two distinct scalar fields. There are two types of Yukawa couplings in this model, and either one or the other of them can be asymptotically free (but not both simultaneously). © 1998 The American Physical Society.

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