Geometry of renormalization group flows in theory space - art. no. 105017

Renormalization group (RG) flows in theory space (the space of couplings) a re generated by a vector field-the beta function. Using a specific metric a nsatz in theory space and certain methods employed largely in the context o f general relativity, we examine the nature of the expansion, shear and rot ation of geodesic RG flows. The expansion turns out to be a negative quanti ty inversely related to the norm of the beta function. This implies the foc using of the flows towards the fixed points of a given field theory. The ev olution equation for the expansion along geodesic RG flows is written down and analyzed. We illustrate the results for a scalar field theory with a j phi coupling and pointers to other areas are briefly mentioned.