Fermionic Field Theory and Gauge Interactions on Random Lattices

TL;DR

This paper investigates how gauge interactions affect fermions on random lattices, revealing that gauge invariance can revive fermion doubling issues even when they are suppressed in free theories.

Contribution

The study introduces a new formulation for fermions on random lattices and compares the behavior of different fermion discretizations in gauge theories, highlighting the role of gauge invariance.

Findings

Doublers are revived on random lattices in the continuum limit.

Gauge invariance is critical in the revival of fermion doubling.

Random lattices do not inherently solve the doubling problem with gauge interactions.

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. However, gauge interactions impose stringent constraints as expressed by the Ward-Takahashi identities which could revive the free-field suppressed doubler modes in loop diagrams. After introducing a formulation for fermions on a new kind of random lattice, we compare random, naive and Wilson fermions in two dimensional Abelian background gauge theory. We show that the doublers are revived for random lattices in the continuum limit, while demonstrating that gauge invariance plays the critical role in this revival. Some implications of the persistent doubling phenomenon on random lattices are also discussed.