A Dual Algorithm for Non-abelian Yang-Mills coupled to Dynamical Fermions

Abstract

We extend the dual algorithm recently described for pure, non-abelian Yang-Mills on the lattice to the case of lattice fermions coupled to Yang-Mills, by constructing an ergodic Metropolis algorithm for dynamic fermions that is local, exact, and built from gauge-invariant boson-fermion coupled configurations. For concreteness, we present in detail the case of three dimensions, for the group SU(2) and staggered fermions, however the algorithm readily generalizes with regard to group and dimension. The treatment of the fermion determinant makes use of a polymer expansion; as with previous proposals making use of the polymer expansion in higher than two dimensions, the critical question for practical applications is whether the presence of negative amplitudes can be managed in the continuum limit.

17 pages, 11 figures

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• A Dual Non-abelian Yang-Mills Amplitude in Four Dimensions
• Duality transformations and the entanglement entropy of gauge theories
• A Gauge-Independent Mechanism for Confinement and Mass Gap: Part I -- The General Framework
• Fermion Bag Approach for Massive Thirring Model at Finite Density
• A Gauge-Independent Mechanism for Confinement and Mass Gap: Part II -- G=SU(2) and D=3
• Comparison between Fermion Bag Approach and Complex Langevin Dynamics for Massive Thirring Model at Finite Density in 0 + 1 Dimensions