Dual Non-Abelian Yang-Mills Simulations in Four Dimensions

Abstract

We present numerical results for pure SU(2) Yang-Mills theory in four space-time dimensions using a novel algorithm based on dually transformed variables. The simulation makes use of a recently derived O(j^4) algorithm for the dual vertex amplitude and a dual Metropolis algorithm that generalizes the one recently developed for three dimensions. The dual algorithm is validated against the equivalent model using conventional variables over a range of couplings, spin cut-offs, and lattice sizes. We consider a lattice size up to 8x8x8x8, where the problem of negative amplitudes renders the simulation results excessively noisy even at a relatively low beta (starting at about beta=1.8). In conclusion, we survey some approaches to addressing the sign problem in this context and increasing the efficiency of dual computations within this approach.