Connecting short to long scales in the confining vacuum

TL;DR

This paper investigates approximate decimations in SU(N) lattice gauge theory to connect short and long-distance regimes, providing bounds on the partition function and insights into deriving confinement from first principles.

Contribution

It introduces a method using bond-moving decimations to bound and represent the exact partition function, linking effective couplings across scales.

Findings

Bond-moving decimations provide bounds on the partition function.

Decimation flows relate to confinement mechanisms.

A framework for deriving confinement from first principles.

Abstract

We study approximate decimations in SU(N) LGT that connect the short to long distance regimes. Simple `bond-moving' decimations turn out to provide both upper and lower bounds on the exact partition function. This leads to a representation of the exact partition function in terms of successive decimations whose effective couplings flows are related to those of the easily computable bond-moving decimations. The implications for a derivation of confinement from first principles are discussed.