Asymptotic symmetries and subleading soft graviton theorem (1408.2228v3)

Abstract: Motivated by the equivalence between soft graviton theorem and Ward identities for the supertranslation symmetries belonging to the BMS group, we propose a new extension (different from the so-called extended BMS) of the BMS group which is a semi-direct product of supertranslations and Diff(S^2). We propose a definition for the canonical generators associated to the smooth diffeomorphisms and show that the resulting Ward identities are equivalent to the subleading soft graviton theorem of Cachazo and Strominger.

• The paper introduces a generalized BMS group that incorporates supertranslations and smooth sphere diffeomorphisms to broaden asymptotic symmetry analysis.
• It derives Ward identities that connect the new symmetry framework with the subleading soft graviton theorem, refining our understanding of gravitational scattering.
• It identifies challenges with the non-closure of charges in the radiative phase space, prompting reconsideration of existing quantum gravity frameworks.

Asymptotic Symmetries and Subleading Soft Graviton Theorem: A Formal Examination

The paper by Campiglia and Laddha proposes a novel extension of the Bondi-Metzner-Sachs (BMS) group, which plays a fundamental role in asymptotically flat spacetimes and has been instrumental in understanding quantum gravity. Unlike the typical extensions involving Virasoro symmetries, the authors introduce the "generalized BMS group," denoted as $G$, which includes supertranslations and smooth diffeomorphisms of the sphere $\text{Diff}(S^2)$. This new group maintains the asymptotic flatness but does not preserve the leading order kinematical metric components, instead permitting arbitrary sphere diffeomorphisms at infinity.

A significant strength of this paper lies in establishing a link between the constraints implied by the new symmetry group and the subleading soft graviton theorem. This theorem, which refines the well-known soft graviton theorem by Weinberg, has been conjectured to enjoy broad applicability in gravitational scattering processes. The authors derive Ward identities for this generalized symmetry, showing their equivalence with the subleading soft graviton theorem of Cachazo and Strominger. This approach is reminiscent of earlier work that connected Weinberg's soft graviton theorem directly with supertranslation symmetry.

The implications for quantum gravity are noteworthy. The authors suggest that the introduction of the generalized BMS group necessitates re-evaluating the radiative phase space description pioneered by Ashtekar. This re-evaluation could lead to a more robust framework for understanding gravitational scattering and the accompanying symmetries. However, the exact interpretation of the proposed Ward identities within a fully systematic analysis remains open, particularly given that their charges do not form a closed algebra, a phenomenon also observed in massless QED studies.

Several challenges inherent in this extension are highlighted, notably the non-closure of the charges under the generalized BMS symmetries. This problem may stem from the underlying framework of the radiative phase space, which is pegged to a fixed space-time metric at leading order in $1/r$. Adjustments to the radiative phase space that relax its dependence on fixed universal structures may offer a solution.

The theoretical ramifications extend into refining our understanding of quantum scattering amplitudes and potentially offering new insights into infrared issues in quantum gravity. Practically, this refined symmetry framework demands future work to consolidate the charges into a cohesive algebra that retains physical significance across scenarios.

In future developments, the generalization of spacetime symmetries introduced in this paper will likely serve as a pivotal point for deeper investigations into the connections between asymptotic symmetries and quantum scattering, offering a richer structure to explore gravitational interactions at both classical and quantum levels. The classroom of quantum gravity will benefit greatly from these insights, facilitating richer explorations into the mathematical elegance and complexity of general relativity’s extensions in quantum domains.