Chiral Lattice Fermions From Staggered Fields

TL;DR

This work proposes a concrete lattice construction to realize chiral fermions by combining reduced staggered fermions with site-parity dependent Fidkowski-Kitaev-type four-fermion interactions, enabling symmetric mass generation that gaps mirror modes without breaking symmetries. The approach leverages a Spin$(7)$ real eight-dimensional representation and anomaly cancellation constraints (notably a discrete spin-$Z_4$ anomaly) to count massless modes correctly in the continuum, aiming to produce Weyl fermions in the infrared. In two dimensions, numerical simulations provide evidence that even-parity modes become heavy while odd-parity modes remain light, hinting at the desired chiral continuum limit; the authors outline a pathway to extend the construction to four dimensions, where the continuum would host $16$ Weyl (or Majorana) fermions and potentially yield a chiral lattice gauge theory upon gauging. The work thus offers a viable route to lattice chiral theories with controlled anomalies and manageable sign problems, subject to further nonperturbative checks in higher dimensions and upon gauging.

Abstract

We describe a proposal for constructing a lattice theory that we argue may be capable of yielding free Weyl fermions in the continuum limit. The model employs reduced staggered fermions and uses site parity dependent Yukawa interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions without breaking symmetries. The possibility for such symmetric mass generation is tied to the cancellation of certain discrete anomalies arising in the continuum limit. The latter place strong constraints on the number of lattice fermions -- constraints that are satisfied by this model. We present numerical results for the model in two dimensions which support this sc

Figures (8)

• Figure 1: Four fermion condensate vs $G$
• Figure 2: $<(\chi^T\Gamma\chi)^2>$ vs $G$ for $L=8,16$
• Figure 3: $<n\epsilon(x)n>$ vs $\lambda_n$ for $8^2$ lattice at $G=5.0$ and $g=0.01$
• Figure 4: Histogram of $<\epsilon(x)>$ for $L=8$ and $G=5.0$, $g=0.01$
• Figure 5: First 32 eigenvalues of the fermion operator for $G=0.01$, $G=0.1$ and $G=1.0$ for $8^2$ lattice at $g=0.01$ and pbc