Phase structure of non-commutative scalar field theories

Details Phase structure of non-commutative scalar field theories Phase structure of non-commutative scalar field theories

2000-06-16

arxiv.org/abs/hep-th/0006119v3

Nucl.Phys. B605 (2001) 395-424

Physics

High Energy Physics

High Energy Physics - Theory

33 pages, latex. v2: minor improvements, version to appear in NPB

Scientific paper

10.1016/S0550-3213(01)00108-0

We investigate the phase structure of non-commutative scalar field theories and find evidence for ordered phases which break translation invariance. A self-consistent one-loop analysis indicates that the transition into these ordered phases is first order. The phase structure and the existence of scaling limits provides an alternative to the structure of counter-terms in determining the renormalizability of non-commutative field theories. On the basis of the existence of a critical point in the closely related planar theory, we argue that there are renormalizable interacting non-commutative scalar field theories in dimensions two and above. We exhibit this renormalization explicitly in the large $N$ limit of a non-commutative O(N) vector model.

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