On the geometry of the theory space in the ERG formalism

TL;DR

This paper explores the geometric structure of theory space in the ERG formalism, introducing connections and invariants to better understand the space of couplings in quantum field theories.

Contribution

It proposes a geometric framework for theory space in the ERG formalism, defining connections and scheme-invariant quantities from ERG solutions.

Findings

Defined a connection on theory space from ERG solutions

Introduced scheme-invariant physical quantities

Provided a geometric interpretation of the ERG formalism

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.