Evidence of Taste-Symmetry restoration for Kähler-Dirac fermions on Euclidean Dynamical Triangulations

Abstract

We study the spectrum of two-particle bound states of Kähler-Dirac fermions coupled via gravity in Euclidean Dynamical Triangulations (EDT). We work in the quenched approximation, where the geometry is allowed to fluctuate, but there is no back-reaction from the matter on the geometry. The Kähler-Dirac action respects an exact $U(1)$ symmetry that is related to continuum chiral symmetry, and this $U(1)$ symmetry ensures that some of the bound-state masses vanish in the chiral limit of vanishing fermion bare mass. The bound-state masses that are not protected by the $U(1)$ symmetry do not vanish in the chiral limit, but the scale associated with the symmetry breaking does not appear to be a physical scale like the Planck mass or the curvature scale of the emergent de Sitter background. Rather, the mass scale associated with this non-degeneracy appears to be a positive power of the lattice spacing, decreasing as the continuum limit is approached. This suggests that Kähler-Dirac fermions in EDT can be interpreted as the gravity analog of staggered fermions in flat-space lattice field theories, with similar behavior.