New symmetries for the Gravitational S-matrix (1502.02318v2)

Abstract: In [15] we proposed a generalization of the BMS group G which is a semidirect product of supertranslations and smooth diffeomorphisms of the conformal sphere. Although an extension of BMS, G is a symmetry group of asymptotically flat space times. By taking G as a candidate symmetry group of the quantum gravity S-matrix, we argued that the Ward identities associated to the generators of Diff(S^2) were equivalent to the Cachazo-Strominger subleading soft graviton theorem. Our argument however was based on a proposed definition of the Diff(S^2) charges which we could not derive from first principles as G does not have a well defined action on the radiative phase space of gravity. Here we fill this gap and provide a first principles derivation of the Diff(S^2) charges. The result of this paper, in conjunction with the results of [4, 15] prove that the leading and subleading soft theorems are equivalent to the Ward identities associated to G.

• The paper demonstrates that the CS subleading soft graviton theorem is equivalent to Ward identities for the gravitational S-matrix with generalized BMS symmetry.
• It extends the traditional BMS framework by including full 2-sphere diffeomorphisms, uncovering deeper symmetry structures in quantum gravity.
• The authors derive a consistent symplectic structure and corresponding charges, enhancing the practical computation of gravitational scattering amplitudes.

Insights on "New Symmetries for the Gravitational S-Matrix"

The paper under discussion, authored by Miguel Campiglia and Alok Laddha, endeavors to elaborate upon the intricate relationship between asymptotic symmetries in quantum gravity and their associated Ward identities. Specifically, it establishes a foundational link between the generalized BMS group, denoted as G, and the Cachazo-Strominger (CS) subleading soft graviton theorem. The authors work to demonstrate that this theorem equivalently represents Ward identities for the gravitational S-matrix when G serves as the underlying symmetry group.

Key Contributions

• Generalized BMS Group: Campiglia and Laddha further develop the concept of the BMS group extending beyond supertranslations and the Lorentz group to encompass the full diffeomorphism group of the 2-sphere, Di▼(S^2). This forms the crux of G, a group structured as a semidirect product of supertranslations and the diffeomorphisms of the conformal sphere.
• Soft Theorems and Ward Identities: Building on previous works, they elucidate that the Ward identities associated with the generators of Di▼(S^2) are precisely equivalent to both the leading and subleading soft graviton theorems. These results consolidate the linkage between classical symmetries and quantum gravitational observations, reinforcing the assertion that these theorems are not just perturbative artifacts but embed fundamental symmetries of the theory.
• Symplectic Structure and Charges: A substantial technical challenge addressed in the paper is the derivation of charges for Di▼(S^2) from first principles. The novel contribution here is the introduction of a symplectic structure on the phase space that is coherent with the classical Einstein-Hilbert action and adapts to the radiative phase space formulation. The derived charges align precisely with those conjectured for the Virasoro group, buttressing the equivalency claims regarding the CS theorem.

Implications and Future Directions

Practically, the synthesis of generalized BMS symmetries with soft theorems reveals a nuanced comprehension of gravitational scattering processes. It implies that computing gravitational amplitudes can inherently leverage these symmetries to reduce complexity and enhance theoretical predictions. Theoretically, this underscores the pertinence of symmetries not merely in simplifying calculations but in exposing deep organizing principles of quantum gravity.

Looking forward, an intriguing avenue for exploration is the incorporation of counterterms to address infrared divergences that emerge in the symplectic form, potentially enlightening the algebraic structure of the symmetry generators. Such refinements could further realize a fully symplectic action of G on the phase space and ensure closure of the associated charges. This improvement would solidify the role of symmetries in shaping the precise landscape of asymptotic physics and quantum gravitational theories.

Conclusion

Campiglia and Laddha's work presents a comprehensive framework linking generalized asymptotic symmetries to soft theorems within quantum gravity, establishing a robust correspondence between geometric structures at null infinity and observable scattering phenomena. Their methodological advancements in deriving symplectic structures and charges mark a pivotal step toward harnessing symmetry principles for theoretical unification and practical computation, foreshadowing profound implications for future gravitational research.