Geodesic Renormalisation Group Flow

Abstract

It is shown that the renormalisation group flow in coupling constant space can be interpreted in terms of a dynamical equation for the couplings analogous to viscous fluid flow under the action of a potential. For free scalar field theory the flow is geodesic in two dimensions, while for $D\ne 2$ it is only geodesic in certain limits, e.g. for vanishing external source. For the 1-D Ising model the renormalisation flow is geodesic when the external magnetic field vanishes.

PlainTeX file, 11 pages, 5 figures

References in corpus (3)

• Connection on the theory space
• The Energy-Momentum Tensor in Field Theory I
• The Energy-Momentum Tensor in Field Theory II

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• Conformal Fisher information metric with torsion
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