Abstract
We consider the theory space as a manifold whose coordinates are given by the couplings appearing in the Wilson action. We discuss how to introduce connections on this theory space. A particularly intriguing connection can be defined directly from the solution of the exact renormalization group (ERG) equation. We advocate a geometric viewpoint that lets us define straightforwardly physically relevant quantities invariant under the changes of a renormalization scheme.
Highlights
The theory space is a key ingredient of our modern understanding of quantum and statistical field theory
The study of the renormalization group (RG) flow of the couplings allows us to define the continuum limit of quantum field theories and to derive the scaling properties of the operators by studying the linearized RG flow around a fixed point [1]
Instead of employing partial derivatives, it is natural to employ covariant derivatives that allow us to write down covariant quantities directly. It is the purpose of this work to show that such a geometric structure, namely, a connection on the tangent space, can naturally be introduced from the exact renormalization group (ERG) flow equation
Summary
Institute für Physik (WA THEP) Johannes-Gutenberg-Universität, Staudingerweg 7, 55099 Mainz, Germany. We consider the theory space as a manifold whose coordinates are given by the couplings appearing in the Wilson action. We discuss how to introduce connections on this theory space. A intriguing connection can be defined directly from the solution of the exact renormalization group (ERG) equation. We advocate a geometric viewpoint that lets us define straightforwardly physically relevant quantities invariant under the changes of a renormalization scheme
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