Lattice Regularization of Reduced Kähler-Dirac Fermions and Connections to Chiral Fermions
SciPost Physics(2023)
摘要
We show how a path integral for reduced Kähler-Dirac fermions suffers
from a phase ambiguity associated with the fermion measure that is an analog of
the measure problem seen for chiral fermions. However, unlike the case of
chiral symmetry, a doubler free lattice action exists which is invariant under
the corresponding onsite symmetry. This allows for a clear diagnosis and
solution to the problem using mirror fermions resulting in a unique gauge
invariant measure. By introducing an appropriate set of Yukawa interactions
which are consistent with 't Hooft anomaly cancellation we conjecture the
mirrors can be decoupled from low energy physics. Moreover, the minimal such
Kähler-Dirac mirror model yields a light sector which corresponds, in the
flat space continuum limit, to the Pati-Salam GUT model.
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