Fixed Points of Nonlinear Sigma Models in d>2

Details Fixed Points of Nonlinear Sigma Models in d>2 Fixed Points of Nonlinear Sigma Models in d>2

2008-10-03

arxiv.org/abs/0810.0715v1

Phys.Lett.B672:280-283,2009

Physics

High Energy Physics

High Energy Physics - Theory

9 pages

Scientific paper

10.1016/j.physletb.2009.01.032

Using Wilsonian methods, we study the renormalization group flow of the Nonlinear Sigma Model in any dimension $d$, restricting our attention to terms with two derivatives. At one loop we always find a Ricci flow. When symmetries completely fix the internal metric, we compute the beta function of the single remaining coupling, without any further approximation. For $d>2$ and positive curvature, there is a nontrivial fixed point, which could be used to define an ultraviolet limit, in spite of the perturbative nonrenormalizability of the theory. Potential applications are briefly mentioned.

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