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 tensor multiplets. We study their
interplay with large gauge transformations for dynamical tensor fields. In a
non-trivial background for the global 1-form symmetry, this leads to an
ambiguity of the effective field theory partition function. This anomaly is
eliminated by the inclusion of BPS strings. However, the non-trivial 1-form
background can induce fractional string charges which are not compatible with
Dirac quantization, and hence the symmetry is absent. The anomalous term
therefore serves as a tool to detect whether the discrete 1-form symmetries are
realized, which we demonstrate in explicit examples originating from string
compactifications. We also corroborate this by finding that a non-trivial
ambiguity is related to states which explicitly break the global 1-form
symmetry, which appear as generally massive excitations of the 6d BPS strings.
For 6d theories consistently coupled to gravity, this ambiguity of the
partition function hints at the presence of a symmetry breaking tower of
states. When the ambiguity is absent, the F-theory realization of the theories
points to the gauging of the 1-form symmetries via the presence of non-trivial
Mordell--Weil torsion.Comment: 46 pages + appendices, 2 figures; v2: typos corrected, references
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