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Defining a Chiral Fermion Theory on a lattice has presented an ongoingchallenge both in Condensed Matter physics and in Lattice Gauge Theory. In thispaper, we demonstrate that a chiral free-fermion theory can live on anultra-local spacetime lattice if we allow the Lagrangian to be non-hermitian.Rather than a violation of unitarity, the non-hermitian structure of ourLagrangian arises because time is discrete, and we show that our model is obeysan elementary unitarity condition: namely, that the norm of the two-pointfunctions conserves probability. Beyond unitarity, our model displays severalsurprising properties: it is formulated directly in Minkowskian time; it hasexactly Lorentz invariant dynamics for all frequencies and momenta (in thelarge volume limit); and it is free from all gauge anomalies, despite theprediction from field theory that it should suffer one. We show that our modelis a discrete time description of a single chiral edge mode of several recentlyproposed $2+1$d Floquet models. That the chiral edge can be treated without therest of the $2+1$d system, even when coupled to a gauge field, implies that theFloquet models are radically different from Integer Quantum Hall models, whichalso support chiral edge modes. Furthermore, the Floquet results imply that ourmodel can be physically realized, which presents an opportunity for gaugetheories to be simulated in a condensed matter or cold atom context. Ourresults present a solution to the `Chiral-fermion problem:' a chiral fieldtheory can indeed be defined on an ultra-local spacetime lattice, and weaddress how our model avoids several no-go arguments.

A Single Right-Moving Free Fermion Mode on an Ultra-Local $1+1$d Spacetime Lattice