Geometry of theory space and RG flows

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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9 pages; to appear in the proceedings of IGQR-I (Dec 17-21, IUCAA, Pune, India) in Mod. Phys. Letts. (special issue)

Scientific paper

10.1142/S0217732302007089

The space of couplings of a given theory is the arena of interest in this article. Equipped with a metric ansatz akin to the Fisher information matrix in the space of parameters in statistics (similar metrics in physics are the Zamolodchikov metric or the O'Connor--Stephens metric) we investigate the geometry of theory space through a study of specific examples. We then look into renormalisation group flows in theory space and make an attempt to characterise such flows via its isotropic expansion, rotation and shear. Consequences arising from the evolution equation for the isotropic expansion are discussed. We conclude by pointing out generalisations and pose some open questions.

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