Dynamical Symmetry Breaking in Spaces with Constant Negative Curvature

Details Dynamical Symmetry Breaking in Spaces with Constant Negative Curvature Dynamical Symmetry Breaking in Spaces with Constant Negative Curvature

1999-04-26

arxiv.org/abs/hep-th/9904180v2

Phys.Rev. D61 (2000) 024013

Physics

High Energy Physics

High Energy Physics - Theory

minor text changes, added new references

Scientific paper

10.1103/PhysRevD.61.024013

By using the Nambu-Jona-Lasinio model, we study dynamical symmetry breaking in spaces with constant negative curvature. We show that the physical reason for zero value of critical coupling value $g_c = 0$ in these spaces is connected with the effective reduction of dimension of spacetime $1 + D \to 1 + 1$ in the infrared region, which takes place for any dimension $1 + D$. Since the Laplace-Beltrami operator has a gap in spaces with constant negative curvature, such an effective reduction for scalar fields is absent and there are not problems with radiative corrections due to scalar fields. Therefore, dynamical symmetry breaking with the effective reduction of the dimension of spacetime for fermions in the infrared region is consistent with the Mermin-Wagner-Coleman theorem, which forbids spontaneous symmetry breaking in (1 + 1)-dimensional spacetime.

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