  Brans-Dicke theory contains an additional propagating mode which causes
homogeneous expansion and contraction of test bodies in transverse directions.
This "breathing" mode is associated with novel memory effects in addition to
those of general relativity. Standard tensor mode memories are related to a
symmetry principle: they are determined by the balance equations corresponding
to the BMS symmetries. In this paper, we show that the leading and subleading
breathing memory effects are determined by the balance equations associated
with the leading and "overleading" asymptotic symmetries of a dual formulation
of the scalar field in terms of a two-form gauge field. The memory effect
causes a transition in the vacuum of the dual gauge theory. These results
highlight the significance of dual charges and the physical role of overleading
asymptotic symmetries.
