Potential Flow Of The Renormalisation Group In A Simple Two Component Model

Details Potential Flow Of The Renormalisation Group In A Simple Two Component Model Potential Flow Of The Renormalisation Group In A Simple Two Component Model

1993-07-03

arxiv.org/abs/hep-th/9307023v1

Mod. Phys. Lett. A8 (1993) 3103-3110

Physics

High Energy Physics

High Energy Physics - Theory

7 pages Typset in PlainTeX, C Version 3.141

Scientific paper

The renormalisation group (RG) flow on the space of couplings of a simple model with two couplings is examined. The model considered is that of a single component scalar field with $\phi^4$ self interaction coupled, via Yukawa coupling, to a fermion in flat four dimensional space. The RG flow on the two dimensional space of couplings, ${\cal G}$, is shown to be derivable from a potential to sixth order in the couplings, which requires two loop calculations of the $\beta$-functions. The identification of a potential requires the introduction of a metric on ${\cal G}$ and it is shown that the metric defined by Zamalodchikov, in terms of two point correlation functions of composite operators, gives potential flow to this order.

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