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.
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BibTeX
@misc{dai2026evidence,
title = {{Evidence of Taste-Symmetry restoration for Kähler-Dirac fermions on Euclidean Dynamical Triangulations}},
author = {Mingwei Dai and Walter Freeman and Mason Grieb and Jack Laiho and Marc Schiffer and Judah Unmuth-Yockey},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13791},
eprint = {2610.13791},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13791},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Evidence of Taste-Symmetry restoration for Kähler-Dirac fermions on Euclidean Dynamical Triangulations
AU - Mingwei Dai
AU - Walter Freeman
AU - Mason Grieb
AU - Jack Laiho
AU - Marc Schiffer
AU - Judah Unmuth-Yockey
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13791
UR - https://arxiv.org/abs/2610.13791
AB - 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.
ER -