One loop beta functions and fixed points in Higher Derivative Sigma Models

Details One loop beta functions and fixed points in Higher Derivative Sigma Models One loop beta functions and fixed points in Higher Derivative Sigma Models

2009-10-06

arxiv.org/abs/0910.0851v1

Phys.Rev.D81:065012,2010

Physics

High Energy Physics

High Energy Physics - Theory

26 pages

Scientific paper

10.1103/PhysRevD.81.065012

We calculate the one loop beta functions for nonlinear sigma models in four dimensions containing general two and four derivative terms. In the O(N) model there are four such terms and nontrivial fixed points exist for all N \geq 4. In the chiral SU(N) models there are in general six couplings, but only five for N=3 and four for N=2; we find fixed points only for N=2,3. In the approximation considered, the four derivative couplings are asymptotically free but the coupling in the two derivative term has a nonzero limit. These results support the hypothesis that certain sigma models may be asymptotically safe.

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