The Nielsen–Ninomiya theorem is a no-go theorem in physics, in particular in lattice gauge theory, concerning the possibility of defining a theory of chiral fermions on a lattice in even dimensions. The theorem can be stated as follows: let
Since the Standard Model is chiral (left- and right-handed fermions are treated differently by weak interactions, for example), the Nielsen–Ninomiya theorem implies that for simulating some Standard Model phenomena at least one of the assumptions of the theorem needs to be violated.