Block renormalization group transformations and overlap fermions

TL;DR

This paper proposes a preliminary argument for a renormalization group transformation that maps continuum fermion actions to Ginsparg-Wilson lattice actions, exemplified by the overlap operator, with potential implications for lattice gauge theory.

Contribution

It introduces a novel renormalization group blocking transformation specifically for Ginsparg-Wilson fermions, particularly the overlap operator, advancing lattice fermion formulation methods.

Findings

Constructed the blocking for the massless overlap operator

Indicated how to derive other Ginsparg-Wilson lattice Dirac operators

Modified gauge action and added irrelevant terms through the transformation

Abstract

In this preliminary work, I provide the outline of an argument (leaving the full proof to a future publication) that there exists a valid renormalization group blocking transformation which converts the continuum fermion action into a Ginsparg-Wilson lattice action. I construct the blocking for the massless overlap operator as a specific example, indicating how other Ginsparg-Wilson lattice Dirac operators can be derived in a similar fashion. This renormalization group transformation modifies the gauge action and adds a number of irrelevant terms to the lattice action. The procedure is not valid for lattice Dirac operators which do not exactly satisfy the Ginsparg-Wilson relation, for example the Wilson operator.