Deriving confinement via RG decimations

TL;DR

This paper introduces a framework using approximate RG decimations to demonstrate that SU(2) lattice gauge theory remains confining across all couplings in up to four dimensions, without fixed points.

Contribution

It develops a novel RG decimation approach that bounds the partition function and shows confinement for all couplings in SU(2) lattice gauge theory.

Findings

SU(2) LGT is confining for all couplings in d ≤ 4

RG decimations constrain the partition function from above and below

Flow from weak to strong coupling without fixed points

Abstract

We present the general framework and building blocks of a recent derivation of the fact that the SU(2) LGT is in a confining phase for all values of the coupling $0 < \beta < \infty$, for space-time dimension $d \leq 4$. The method employs approximate but explicitly computable RG decimations that are shown to constrain the exact partition function and order parameters from above and below, and flow from the weak to the strong coupling regime without encountering a fixed point.