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We consider the theory space as a manifold whose coordinates are given by thecouplings appearing in the Wilson action. We discuss how to introduceconnections on this theory space. A particularly intriguing connection can bedefined directly from the solution of the exact renormalization group (ERG)equation. We advocate a geometric viewpoint that lets us definestraightforwardly physically relevant quantities invariant under the changes ofa renormalization scheme.

On the geometry of the theory space in the ERG formalism