  We describe general methods for determining higher-form symmetry groups of
known 5d and 6d superconformal field theories (SCFTs), and 6d little string
theories (LSTs). The 6d theories can be described as supersymmetric gauge
theories in 6d which include both ordinary non-abelian 1-form gauge fields and
also abelian 2-form gauge fields. Similarly, the 5d theories can also be often
described as supersymmetric non-abelian gauge theories in 5d. Naively, the
1-form symmetry of these 6d and 5d theories is captured by those elements of
the center of ordinary gauge group which leave the matter content of the gauge
theory invariant. However, an interesting subtlety is presented by the fact
that some massive BPS excitations, which includes the BPS instantons, are
charged under the center of the gauge group, thus resulting in a further
reduction of the 1-form symmetry. We use the geometric construction of these
theories in M/F-theory to determine the charges of these BPS excitations under
the center. We also provide an independent algorithm for the determination of
1-form symmetry for 5d theories that admit a generalized toric construction.
The 2-form symmetry group of 6d theories, on the other hand, is captured by
those elements of the center of the abelian 2-form gauge group that leave all
the massive BPS string excitations invariant, which is much more
straightforward to compute as it is encoded in the Green-Schwarz coupling
associated to the 6d theory.
