Low Energy Spectrum of SU(2) Lattice Gauge Theory: An Alternate Proposal via Loop Formulation

TL;DR

This paper introduces a novel loop formulation for SU(2) lattice gauge theory that simplifies the analysis of low energy spectra, revealing phase transitions and matching known results in the weak coupling regime.

Contribution

It presents a new prepotential-based loop formulation on honeycomb lattices, extending to arbitrary dimensions, and develops a mean field approach with a reduced Hamiltonian for easier spectrum computation.

Findings

Identifies two phases with a first order transition at g=1.

Derives a reduced Hamiltonian matching existing spectral results.

Proposes an easier computational framework for low energy spectra.

Abstract

We show that, prepotential formulation of gauge theories on honeycomb lattice yields local loop states, which are free from any spurious loop degrees of freedom and hence exact and orthonormal. We also illustrate that, the dynamics of orthonormal loop states are exactly same in both the square and honeycomb lattices. We further extend this construction to arbitrary dimensions. Utilizing this result, we make a mean field ansatz for loop configurations for SU(2) lattice gauge theory in $2+1$ dimension contributing to the low energy sector of the spectrum. Using variational analysis, we show that, this type of mean loop configurations has two distinct phases in the strong and weak coupling regime and shows a first order transition at $g=1$. We then propose a reduced Hamiltonian to describe the dynamics of the theory within the mean field ansatz. We further work with the mean loop configuration obtained at the weak coupling regime and analytically calculate the spectrum of the reduced Hamiltonian. The spectrum matches with that of the existing literature in this regime, establishing our ansatz to be a valid alternate one which is far more easier to handle for computation.