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

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