RG Decimations and Confinement

TL;DR

This paper demonstrates that SU(2) gauge theory remains in a confining phase across all coupling values by deriving bounds on partition functions using decimation transformations.

Contribution

It introduces a method to establish confinement in SU(2) gauge theory through bounding decimation transformations, providing a rigorous analytical approach.

Findings

SU(2) gauge theory is confining for all couplings

Bounds on partition functions constrain the theory's phase

Decimation transformations facilitate analytical bounds

Abstract

We outline the steps in a derivation of the statement that the SU(2) gauge theory is in a confining phase for all values of the coupling, $0 < \beta <\infty$, defined at lattice spacing a. The approach employed is to obtain both upper and lower bounds for the partition function and the `twisted' partition function in terms of approximate decimation transformations. The behavior of the exact quantities is thus constrained by that of the easily computable bounding decimations.