Theoretical and Computational Aspects of New Lattice Fermion Formulations

Abstract: In this work we investigate theoretical and computational aspects of novel lattice fermion formulations for the simulation of lattice gauge theories. The lattice approach to quantum gauge theories is an important tool for studying quantum chromodynamics, where it is the only known framework for calculating physical observables from first principles. In our investigations we focus on staggered Wilson fermions and the related staggered domain wall and staggered overlap formulations. Originally proposed by Adams, these new fermion discretizations bear the potential to reduce the computational costs of state-of-the-art Monte Carlo simulations. Staggered Wilson fermions combine aspects of both staggered and Wilson fermions while having a reduced number of fermion doublers compared to usual staggered fermions. Moreover, they can be used as a kernel operator for the domain wall fermion construction with potentially significantly improved chiral properties and for the overlap operator with its exact chiral symmetry. This allows the implementation of chirality on the lattice in a controlled manner at potentially significantly reduced costs. The practical potential and limitations of these new lattice fermions are also critically discussed.