Higher-form symmetries of 6d and 5d theories

<jats:title>A<jats:sc>bstract</jats:sc>
</jats:title><jats:p>We describe general methods for determining higher-form symmetry groups of known 5<jats:italic>d</jats:italic> and 6<jats:italic>d</jats:italic> superconformal field theories (SCFTs), and 6<jats:italic>d</jats:italic> little string theories (LSTs). The 6<jats:italic>d</jats:italic> theories can be described as supersymmetric gauge theories in 6<jats:italic>d</jats:italic> which include both ordinary non-abelian 1-form gauge fields and also abelian 2-form gauge fields. Similarly, the 5<jats:italic>d</jats:italic> theories can also be often described as supersymmetric non-abelian gauge theories in 5<jats:italic>d</jats:italic>. Naively, the 1-form symmetry of these 6<jats:italic>d</jats:italic> and 5<jats:italic>d</jats:italic> 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 5<jats:italic>d</jats:italic> theories that admit a generalized toric construction (i.e. a 5-brane web construction). The 2-form symmetry group of 6<jats:italic>d</jats:italic> 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 6<jats:italic>d</jats:italic> theory.</jats:p>