Comparing memory effects in gravity and gauge theories

The study of memory effects in gravity and gauge theories produced insights into the infrared dynamics of these theories and their asymptotic symmetries and conservation laws. In this talk, we will introduce and compare a hierarchy of memory effects in gravity, electromagnetism, and non-abelian Yang-Mills theory. In gravity, memory effects are related to a lasting change, after a burst of gravitational waves, in the relative separation of test masses. The hierarchy of memory effects arises in the dependence of this displacement on the initial displacement, velocity, or acceleration (and its time derivatives) of the masses. There is also a hierarchy of electromagnetic memory effects. They are determined by a change in the momentum of test charges, following a burst of electromagnetic waves, which depends on initial velocity, or acceleration and its time derivatives. In classical Yang-Mills theory, there is an analogous memory hierarchy in the momentum change for non-abelian charges after a burst of Yang-Mills radiation. We compute the hierarchy of memory effects in these three theories from their asymptotic field equations. We determine the "charge" and "flux" contributions to the memory effects and interpret their similarities and differences in these theories.