Lattice QCD as a theory of interacting surfaces

TL;DR

This paper reformulates pure gauge lattice QCD in arbitrary dimensions as a theory of interacting surfaces, providing exact expressions for boundary functionals and expressing partition functions and observables as averages over surface configurations.

Contribution

It introduces a novel surface-based representation of lattice QCD, revealing interactions proportional to surface areas and deriving exact boundary functionals.

Findings

Surface interactions proportional to common area.

Exact boundary functional expressions derived.

Partition functions as averages over surface configurations.

Abstract

Pure gauge lattice QCD at arbitrary D is considered. Exact integration over link variables in an arbitrary D-volume leads naturally to an appearance of a set of surfaces filling the volume and gives an exact expression for functional of their boundaries. The interaction between each two surfaces is proportional to their common area and is realized by a non-local matrix differential operator acting on their boundaries. The surface self-interaction is given by the QCD$_2$ functional of boundary. Partition functions and observables (Wilson loop averages) are written as an averages over all configurations of an integer-valued field living on a surfaces.