Additive and multiplicative renormalization of topological charge with improved gluon/fermion actions: A test case for 3-loop vacuum calculations, using overlap or clover fermions

TL;DR

This paper computes the perturbative renormalization of the topological charge on the lattice using improved gluon and fermion actions, including a first 3-loop calculation with overlap fermions, to test lattice perturbation theory techniques.

Contribution

It presents the first 3-loop computation of the additive renormalization of the topological susceptibility with overlap fermions, advancing lattice perturbation theory methods.

Findings

Calculated one-loop multiplicative renormalization of topological charge density.

Computed three-loop power divergent additive renormalization of topological susceptibility.

Tested techniques and limitations of lattice perturbation theory with overlap fermions.

Abstract

We calculate perturbative renormalization properties of the topological charge, using the standard lattice discretization given by a product of twisted plaquettes. We use the overlap and clover action for fermions, and the Symanzik improved gluon action for 4- and 6-link loops. We compute the multiplicative renormalization of the topological charge density to one loop; this involves only the gluon part of the action. The power divergent additive renormalization of the topological susceptibility is calculated to 3 loops. Our work serves also as a test case of the techniques and limitations of lattice perturbation theory, it being the first 3-loop computation in the literature involving overlap fermions.