Symmetries of Abelian Chern-Simons Theories and Arithmetic

Understand

We determine the unitary and anti-unitary Lagrangian and quantum symmetries of arbitrary abelian Chern-Simons theories.

• The symmetries depend sensitively on the arithmetic properties (e.g.
• prime factorization) of the matrix of Chern-Simons levels, revealing interesting connections with number theory.
• We give a complete characterization of the symmetries of abelian topological field theories and along the way find many theories that are non-trivially time-reversal invariant by virtue of a quantum symmetry, including $U(1)_k$ Chern-Simons theory and $(\mathbb Z_k)_\ell$ gauge theories.