$p$-form gauge fields: charges and memories

Abstract: In this thesis, we study the asymptotic structure of $p$-form theories on flat space. $p$-form theories are generalizations of Maxwell's theory of electrodynamics in which the gauge potential is a higher-rank differential form. As in the Maxwell theory, there is a choice of boundary conditions with an infinite-dimensional asymptotic symmetry group. For higher $p$-form theories on $(2p+2)$-dimensional flat spacetime, the surface charges are classified by the Hodge decomposition of gauge parameters on $2p$-sphere into exact and co-exact charges. For the exact parameters which are special features of higher-form theories, the surface charges are non-commuting. In presence of $p$-branes, there are non-trivial zero-mode charges analogous to the electric charge for point particles. Although our $p$-form discussion is restricted to $2p+2$ dimensions, we generalize the study of Maxwell theory not only to general dimensions but also to the anti-de Sitter background. Finally, motivated by the IR triangle of gauge theories that relate asymptotic symmetries, memory effects, and soft theorems, we introduce a new kind of memory effect exerted on the internal modes of closed and open strings. On closed string probes, soft 2-form radiation rotates left- and right-moving modes oppositely, which amounts to a unit shift in the spin of probe particles. This provides the first instance of an `internal memory effect' on a non-local object. We conclude by general remarks on the physical significance of soft modes.