Symmetries and Anomalies of Hamiltonian Staggered Fermions

TL;DR

This paper analyzes the symmetries and anomalies of Hamiltonian staggered fermions, revealing non-trivial commutation relations and lattice 't Hooft anomalies related to continuum symmetries in (3+1) dimensions.

Contribution

It systematically constructs symmetry operators for staggered fermions and links their algebraic properties to the presence of lattice 't Hooft anomalies.

Findings

Odd multiple shifts anti-commute with time reversal.

Presence of non-trivial commutation relations implies lattice 't Hooft anomalies.

Constructed conserved charges generate symmetries that do not always commute, indicating further anomalies.

Abstract

We review the shift (translation) and time reversal symmetries of Hamiltonian staggered fermions and their connection to continuum symmetries concentrating in particular on the case of massless fermions and (3+1) dimensions. We construct operators using the staggered fields that implement these symmetries on finite lattices. We show that shifts composed of an odd multiple of the elementary shift anti-commute with time reversal and are related to continuum axial transformations. We argue that the presence of these non-trivial commutation relations implies the existence of lattice 't Hooft anomalies. From the shifts we also construct a set of conserved, quantized charges that generate continuous symmetries of the lattice theory. In general these do not commute with the vector charge signaling further 't Hooft anomalies.