RG decimation-based approach to confinement and computation on coarser lattices

TL;DR

This paper introduces a systematic RG decimation method for lattice gauge theory that connects short and long scales, enabling the calculation of physical quantities on coarser lattices and demonstrating confinement in SU(2).

Contribution

It presents a novel RG decimation approach that provides bounds and interpolations for the partition function, facilitating analysis across different lattice scales.

Findings

Provides bounds on the partition function using approximate decimations.

Enables calculation of physical quantities on coarser lattices.

Shows SU(2) flows into the confining strong coupling regime for any initial β.

Abstract

A systematic procedure is presented for connecting short to long scales in LGT. Approximate decimations are used which can provide both upper and lower bounds on the partition function. Its exact value is then obtained by interpolation between the bounds. By iterating the procedure representations of the partition function as well as other physical quantities can be obtained on progressively coarser lattices. For SU(2) IR flow into the confining strong coupling regime results for any initial $\beta$.