Kähler-Dirac fermions on Euclidean dynamical triangulations

Abstract

We study Kähler-Dirac fermions on Euclidean dynamical triangulations. This fermion formulation furnishes a natural extension of staggered fermions to random geometries without requring vielbeins and spin connections. 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. By examining the eigenvalue spectrum and the masses of scalar mesons we find evidence for a four fold degeneracy in the fermion spectrum in the large volume, continuum limit. It is natural to associate this degeneracy with the well known equivalence in continuum flat space between the Kähler-Dirac fermion and four copies of a Dirac fermion. Lattice effects then lift this degeneracy in a manner similar to staggered fermions on regular lattices. The evidence that these discretization effects vanish in the continuum limit suggests both that lattice continuum Kähler-Dirac fermions are recovered at that point, and that this limit truly corresponds to smooth continuum geometries. One additional advantage of the Kähler-Dirac action is that it respects an exact $U(1)$ symmetry on any random triangulation. This $U(1)$ symmetry is related to continuum chiral symmetry. By examining fermion bilinear condensates we find strong evidence that this $U(1)$ symmetry is not spontaneously broken in the model at order the Planck scale. This is a necessary requirement if models based on dynamical triangulations are to provide a valid ultraviolet complete formulation of quantum gravity.

12 pages, 9 figures, 1 table

References in corpus (6)

• Asymptotic safety in higher-derivative gravity
• Ultraviolet properties of f(R)-Gravity
• The Nonperturbative Quantum de Sitter Universe
• Dimension and Dimensional Reduction in Quantum Gravity
• Lattice Quantum Gravity and Asymptotic Safety
• Topological fermion condensates from anomalies

Cited by in corpus (17)

• Light charged fermions in quantum gravity
• Lattice Setup for Quantum Field Theory in AdS${}_2$
• Predictive power of grand unification from quantum gravity
• The de Sitter Instanton from Euclidean Dynamical Triangulations
• 't Hooft anomalies for staggered fermions
• Are there ALPs in the asymptotically safe landscape?
• A curvature bound from gravitational catalysis in thermal backgrounds
• Hyperbolic Lattice for Scalar Field Theory in AdS${}_3$
• Newtonian Binding from Lattice Quantum Gravity
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Scalar fields in Causal Dynamical Triangulations
• Shift-symmetric Horndeski gravity in the asymptotic-safety paradigm
• The Planar Thirring Model with Kähler-Dirac Fermions
• Lattice regularizations of $\theta$ vacua: Anomalies and qubit models
• Lattice Regularization of Reduced Kähler-Dirac Fermions and Connections to Chiral Fermions
• The weak-gravity bound and the need for spin in asymptotically safe matter-gravity models
• Three models of non-perturbative quantum-gravitational binding