Burg-Metzner-Sachs symmetry, string theory, and soft theorems

Abstract

We study the action of the BMS group in critical, bosonic string theory living on a target space of the formand C is an arbitrary compactification. We provide a treatment of generalized WardTakahashi identities and derive consistent boundary conditions for any d from string theory considerations. Finally, we derive BMS transformations in higher dimensional spacetimes and show that the generalized Ward-Takahashi identity of BMS produces Weinberg's soft theorem in string theory.

BMS supertranslation symmetry implies Faddeev-Kulish amplitudes

“…We are interested in these expressions at the leading terms in the large-r expansion which are known to be gauge-invariant [21]. The action of the hard charge Q H on a Fock state of N massive particles can be expressed as [20] …”

Gravitational memory in higher dimensions

“…The utility of this gauge choice in the context of the IR triangle was originally suggested in [19].…”

Asymptotic dynamics in perturbative quantum gravity and BMS supertranslations

“…We would now like to express the generator of soft supertranslations in terms of the creation and annihilation operators. To do this, we will be using the results of [22,23], where it was shown that to leading order in the asymptotic expansion, the soft supertranslations generator is gauge-invariant. Therefore, instead of performing the computation in the general Gupta-Bleuler quantization that we have been using so far, we can go further and fix the residual gauge freedom left after setting the harmonic gauge.…”

“…As explained above, that will not change the result since, to leading order in the asymptotic expansion, the soft supertranslation generator is independent of the gauge choice [22,23]. Using this and the plane wave expansion (for example see appendix A of [13]), we write the radiative data as [10] …”