Generalised symmetries in the axiverse

The thesis investigates the generalised global symmetries in an Axion-Maxwell model and in an extended version with more axions and U(1) gauge fields. Generalised symmetries are q-form global symmetries acting on charged operators O(X), supported on q-dimensional spacetime manifolds, and are generated by operators U_g(Σ), supported on (d − q − 1)-dimensional manifolds. In particular, the main focus is on non-invertible global symmetries. These arise from exponentiating a current that is no longer conserved by the theory (for example, due to the introduction of a new interaction) and attaching to the resulting operator the partition function of a TQFT ("topological quantum field theory") living on the same submanifold. The partition function of the TQFT accounts for the additional term in the current conservation law generated by the new interaction. The applications of these studies concern the hierarchy of energy scales at which these symmetries are expected to be broken according to the "no global symmetry conjecture". Some of these symmetries are subordinate to others, in the sense that they cannot exist if the latter are broken. This hierarchical structure is reflected in the non-invertible global symmetries obtained through the half-higher gauging procedure. Finally, we study a possible potential for the axion field generated by monopoles, which breaks the shift symmetry, and discuss the regime in which this potential becomes relevant.