Lattice Regularization of Reduced Kähler-Dirac Fermions and Connections to Chiral Fermions

Abstract

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.

13 pages. Minor revision to text

References in corpus (13)

• Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
• Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
• Symmetric Mass Generation
• Massive fermions without fermion bilinear condensates
• Interacting Topological Insulator and Emergent Grand Unified Theory
• Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Model
• Gapped Chiral Fermions
• Anomalies and symmetric mass generation for Kaehler-Dirac fermions
• Generating a non-perturbative mass gap using Feynman diagrams in an asymptotically free theory
• 't Hooft anomalies for staggered fermions
• Chiral Lattice Fermions From Staggered Fields
• Induced topological gravity and anomaly inflow from Kaehler-Dirac fermions in odd dimensions
• Lattice chirality, anomaly matching, and more on the (non)decoupling of mirror fermions