Abstract
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.
Highlights
Let us consider a theory of two form field BBμν dxμdxν with the Lagrangian L= H ∧ ∗H, where dB is the corresponding field strength.3The field equation and the Bianchi identity read d ∗ H = 0, dH = 0, (3.1)which imply respectively that
Standard tensor mode memories are related to a symmetry principle: they are determined by the balance equations corresponding to the BMS symmetries
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
Summary
Physical distances are measured by the metric gμν and matter fields are supposed to be minimally coupled to this metric. We do not include matter fields in the action, as our analysis will be in the far zone where matter fields are not present. Adding electromagnetic field is possible and will not alter the field equations for the scalar λ as the electromagnetic stress tensor is traceless. The corrections to the metric are mostly subleading except certain contributions which can be added a posteriori
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