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

Authors
Citation
S. Kar, Geometry of renormalization group flows in theory space - art. no. 105017, PHYS REV D, 6410(10), 2001, pp. 5017
Citations number
13
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW D
ISSN journal
05562821 → ACNP
Volume
6410
Issue
10
Year of publication
2001
Database
ISI
SICI code
0556-2821(20011115)6410:10<5017:GORGFI>2.0.ZU;2-T
Abstract
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.