A renormalisation group derivation of the overlap formulation

TL;DR

This paper derives the lattice overlap fermion action from the continuum Dirac operator using a renormalisation group approach, establishing a connection between continuum and lattice chiral symmetry.

Contribution

It presents a novel renormalisation group blocking method that produces the overlap fermion action from the continuum, and derives the Ginsparg-Wilson equations and lattice chiral symmetry.

Findings

Constructed a local, valid renormalisation group blocking for overlap fermions.

Derived the Ginsparg-Wilson equations from the continuum.

Outlined a potential approach for lattice chiral gauge theories.

Abstract

Starting from the continuum Dirac operator, I construct a renormalisation group blocking which transforms the continuum action into a lattice action, and I specifically consider the Wilson and overlap formalisms. For Wilson fermions the inverse blocking is non-local and thus invalid. However, I proceed to demonstrate that it is possible to construct a valid, local, blocking which, though dependent on the lattice spacing, generates the lattice overlap fermion action from the continuum action. Using this renormalisation group blocking for overlap fermions, I derive the Ginsparg-Wilson equations and the lattice chiral symmetry. I suggest how the construction of a lattice chiral gauge theory could follow naturally from this approach.