  Recently introduced generalized global symmetries have been useful in order
to understand non-perturbative aspects of quantum field theories in four and
lower dimensions. In this paper we focus on 1-form symmetries of weakly coupled
6d supersymmetric gauge theories coupled to dynamical tensor multiplets. We
study the consistency of global 1-form symmetries corresponding to the center
of the gauge groups, or subgroups thereof, by activating their background
fields, which makes the instanton density fractional. In 6d, an instanton
background for a given gauge theory sources BPS strings via tadpole
cancellation. The non-trivial 1-form symmetry background configurations
contribute to the charge of the BPS strings. However, Dirac quantization
imposes restrictions on the consistent 1-form backgrounds, since they can in
general lead to and induce fractional charges, thus making (part of) the
putative higher-form symmetry inconsistent. This gives explicit criteria to
determine whether the discrete 1-form symmetries are realized. We implement
these criteria in concrete examples originating from string compactifications.
We also corroborate this by finding that a non-trivial fractional contribution
is related to states which explicitly break the global 1-form symmetry
appearing as massive excitations of the 6d BPS strings. For 6d theories
consistently coupled to gravity, this hints at a symmetry breaking tower of
states. When the fractional contributions are absent, the F-theory realization
of the theories points to the gauging of the 1-form symmetry via the presence
of non-trivial Mordell--Weil torsion.
