Real space renormalization group for twisted lattice N=4 super Yang-Mills

TL;DR

This paper develops a real space renormalization group scheme for twisted lattice N=4 super Yang-Mills theory, demonstrating its preservation of lattice structure and symmetries, and illustrating its use through Monte Carlo calculations.

Contribution

It provides an explicit blocking scheme that maintains lattice structure and symmetries, enabling analysis of the long-distance effective action of the theory.

Findings

Explicit real space RG scheme preserving lattice symmetries

Practical Monte Carlo implementation demonstrated

Implications for understanding long-distance behavior

Abstract

A necessary ingredient for our previous results on the form of the long distance effective action of the twisted lattice N=4 super Yang-Mills theory is the existence of a real space renormalization group which preserves the lattice structure, both the symmetries and the geometric interpretation of the fields. In this brief article we provide an explicit example of such a blocking scheme and illustrate its practicality in the context of a small scale Monte Carlo renormalization group calculation. We also discuss the implications of this result, and the possible ways in which to use it in order to obtain further information about the long distance theory.