Subleading Soft Theorem in Arbitrary Dimension from Scattering Equations
This paper presents a significant advancement in the understanding of soft graviton theorems by addressing their applicability in arbitrary dimensions. Specifically, the authors use the CHY (Cachazo-He-Yuan) formula to demonstrate the universality of subleading soft graviton theorems for both Yang-Mills theory and gravity at tree level. This work builds on previously proposed conjectures regarding the symmetry principles underlying soft theorems.
Key Points and Findings
- Soft Theorems and BMS Symmetry: The paper begins by situating the work within the context of Strominger's proposal that links infinite-dimensional symmetries to the behavior of the quantum gravity S-matrix. Here, Weinberg's soft theorem is interpreted as a Ward identity for an infinite-dimensional subgroup of Bondi-Metzner-Sachs supertranslations. Extending this framework, the authors focus on a conjectured subleading soft graviton theorem, initially stated to be universal.
- Tree-level Verification using CHY Formula: In an ambitious leap, this paper extends the verification of subleading soft theorems to arbitrary dimensions using the CHY formula for scattering amplitudes. This formula provides a compact representation of tree-level amplitudes in scalar, gauge, and gravity theories, supported by the scattering equations approach. Importantly, the authors leverage this formulation to demonstrate the dimensional independence of the subleading soft factors.
- Implications Across Dimensions: Demonstratively, the subleading soft factors derived from the CHY integral do not explicitly reference dimensions, a seemingly paradoxical result given the symmetry principles foundational to their original conjecture are inherently four-dimensional. Nonetheless, the numerical results and algebraic derivations support these findings, prompting further inquiry into the dimensional characteristics of symmetry principles.
Implications and Future Directions
The theoretical implications of these findings are profound as they suggest a dimensional robustness in the formulation of soft theorems, potentially broadening the scope of their applicability across theoretical physics and cosmology. Practically, this could influence the computational strategies utilized in high-energy physics, especially in efforts to simulate or analytically resolve particle interactions governed by Yang-Mills and gravitational theories.
Future developments may include extending this tree-level analysis to incorporate loop corrections, potentially unveiling new insights into the intricate symmetries governing particle physics. The authors suggest recent progress in formulating a stringy action principle for CHY amplitudes might pave the way for uncovering the symmetry principles in dimensions beyond the traditional four.
Conclusion
In conclusion, by utilizing the CHY formula, Schwab and Volovich effectively demonstrate the subleading soft theorem's universality across dimensions. This paper exemplifies both the power and potential of leveraging algebraic and integral formulations to extrapolate theoretical results, potentially redefining existing paradigms within the field of theoretical physics.