Perturbative renormalization of lattice N=4 super Yang-Mills theory

TL;DR

This paper demonstrates that a lattice formulation of N=4 super Yang-Mills theory with exact supersymmetry at finite lattice spacing requires only minimal renormalization, simplifying the approach to the continuum limit.

Contribution

It shows that the lattice theory's symmetries prevent unwanted counterterms, ensuring only wavefunction renormalization at one loop, which simplifies continuum limit restoration.

Findings

No mass terms are generated at any finite order.

One-loop divergences can be absorbed by a single wavefunction renormalization.

Only finite part fine-tuning is needed to restore full supersymmetry.

Abstract

We consider N=4 super Yang-Mills theory on a four-dimensional lattice. The lattice formulation under consideration retains one exact supersymmetry at non-zero lattice spacing. We show that this feature combined with gauge invariance and the large point group symmetry of the lattice theory ensures that the only counterterms that appear at any order in perturbation theory correspond to renormalizations of existing terms in the bare lattice action. In particular we find that no mass terms are generated at any finite order of perturbation theory. We calculate these renormalizations by examining the fermion and auxiliary boson self energies at one loop and find that they all exhibit a common logarithmic divergence which can be absorbed by a single wavefunction renormalization. This finding implies that at one loop only a fine tuning of the finite parts is required to regain full supersymmetry in the continuum limit.