We study 't Hooft anomalies for a global discrete internal symmetry G. We construct examples of bosonic field theories in three dimensions with a nonvanishing 't Hooft anomaly for a discrete global symmetry. We also construct field theories in three dimensions with a global discrete internal symmetry G(1) × G(2) such that gauging G(1) necessarily breaks G(2) and vice versa. This is analogous to...

In the turbulence that takes place in rotating fluids, the symmetry assumptions of the theory of fully developed turbulence may not hold, in particular, isotropy must be relaxed to axial symmetry. This symmetry reduction leads one to consider the most general axisymmetric viscosity tensor for a Newtonian fluid, which can be obtained by group theory methods. This tensor generates new turbulent e...

A study of two-dimensional QCD on a spatial circle with Majorana fermions in the adjoint representation of the gauge groups SU(2) and SU(3) has been performed. The main emphasis is put on the symmetry properties related to the homotopically non-trivial gauge transformations and the discrete axial symmetry of this model. Within a gauge fixed canonical framework, the delicate interplay of topolog...

The symmetry number of a tree is defined as the number of nodes of the maximum subtree of the tree that exhibits axial symmetry. The best previous algorithm for computing the symmetry number for an unrooted unordered tree is due to Mitra et al. [8] and runs in O(n) time. In this paper we show an improvement on this time complexity by encoding small trees. Our algorithm runs in time O(n(log logn...

We study ’t Hooft anomalies for a global discrete internal symmetry G. We construct examples of bosonic field theories in three dimensions with a nonvanishing ’t Hooft anomaly for a discrete global symmetry. We also construct field theories in three dimensions with a global discrete internal symmetry G1 × G2 such that gauging G1 necessarily breaks G2 and vice versa. This is analogous to the Adl...

Lattice gauge theories with Wilson fermions break chiral symmetry. In the U(1) axial vector current this manifests itself in the anomaly. On the other hand it is generally expected that the axial vector flavour mixing current is non-anomalous. We give a short, but strict proof of this to all orders of perturbation theory, and show that chiral symmetry restauration implies a unique multiplicativ...