Vacuum Structure of Twisted Scalar Field Theories on M^{D-1} \otimes S^1

Details Vacuum Structure of Twisted Scalar Field Theories on M^{D-1} \otimes S^1 Vacuum Structure of Twisted Scalar Field Theories on M^{D-1} \otimes S^1

2000-10-31

arxiv.org/abs/hep-th/0010283v2

Phys.Rev. D63 (2001) 105003

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, 4 figures, LaTex2e

Scientific paper

10.1103/PhysRevD.63.105003

We study scalar field theories on M^{D-1} \otimes S^1, which allow to impose twisted boundary conditions for the S^1 direction, in detail and report several interesting properties overlooked so far. One of characteristic features is the appearance of critical radii of the circle S^1. A phase transition can occur at the classical level or can be caused by quantum effects. Radiative corrections can restore broken symmetries or can break symmetries for small radius. A surprising feature is that the translational invariance for the S^1 direction can spontaneously be broken. A particular class of coordinate-dependent vacuum configurations is clarified and the O(N) \phi^4 model on M^{D-1}\otimes S^1 is extensively studied, as an illustrative example.

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