The geometry of RG flows in theory space

Details The geometry of RG flows in theory space The geometry of RG flows in theory space

2001-03-05

arxiv.org/abs/hep-th/0103025v1

Phys.Rev. D64 (2001) 105017

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, RevTex, no figures

Scientific paper

10.1103/PhysRevD.64.105017

Renormalisation Group (RG) flows in theory space (the space of couplings) are generated by a vector field -- the $\beta$ function. Using a specific metric ansatz in theory space and certain methods employed largely in the context of General Relativity, we examine the nature of the expansion, shear and rotation of geodesic RG flows. The expansion turns out to be a negative quantity inversely related to the norm of the $\beta$ function. This implies the focusing of the flows towards the fixed points of a given field theory. The evolution equation for the expansion along geodesic RG flows is written down and analysed. We illustrate the results for a scalar field theory with a $j\phi$ coupling and pointers to other areas are briefly mentioned.

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