Fermion Doubling and Gauge Invariance on Random Lattices

TL;DR

This paper investigates the fermion doubling problem on random lattices with gauge interactions, showing that doublers reappear in the continuum limit, which challenges their suitability for gauge theories.

Contribution

It demonstrates that gauge interactions cause fermion doublers to reemerge on random lattices, contrasting with the free-field case where doublers are suppressed.

Findings

Doublers are revived in the continuum limit with gauge interactions.

Random lattices do not inherently solve the fermion doubling problem in gauge theories.

Comparison with naive and Wilson fermions highlights the limitations of random lattices.

Abstract

Random-lattice fermions have been shown to be free of the doubling problem if there are no interactions or interactions of a non-gauge nature. On the other hand, gauge interactions impose stringent constraints as expressed by the Ward-Takahashi identities which could revive the free-field suppressed doubler modes in loop diagrams. Comparing random lattice, naive and Wilson fermions in two dimensional abelian background gauge theory, we show that indeed the doublers are revived for random lattices in the continuum limit. Some implications of the persistent doubling phenomenon on random lattices are also discussed.