Prepotential Formulation of Lattice Gauge Theory

TL;DR

This paper introduces a prepotential-based Hamiltonian formulation for lattice gauge theories, enabling local loop operator construction, diagrammatic rules, and new fusion variables to better analyze weak coupling regimes.

Contribution

It presents a novel prepotential framework with diagrammatic rules and fusion variables for lattice gauge theories, enhancing analysis of weak coupling limits.

Findings

Constructed local loop operators and states using prepotentials.

Developed diagrammatic rules for gauge-invariant operators.

Introduced fusion variables suitable for weak coupling analysis.

Abstract

Within the Hamiltonian formulation of Lattice gauge theories, prepotentials, belonging to the fundamental representation of the gauge group and defined locally at each site of the lattice, enables us to construct local loop operators and loop states. We propose a set of diagrammatic rules for the action of local gauge invariant operators on arbitrary loop states. Moreover We propose a new set of fusion variables within the prepotential aproach suitable for approaching the weak coupling limit.