Holographic Symmetry Algebras for Gauge Theory and Gravity (2103.03961v2)

Abstract: All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D currents acting on the celestial sphere. A complete classification of these symmetries and their algebras is an open problem. Here we construct two towers of such 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights. These generate the symmetries associated to an infinite tower of conformally soft theorems. The current algebra commutators are explicitly derived from the poles in the OPE coefficients, and found to comprise a rich closed subalgebra of the complete symmetry algebra.

A Detailed Examination of Holographic Symmetry Algebras in Gauge Theory and Gravity

In the exploration of gauge and gravitational theories within asymptotically flat spacetimes, the understanding of non-trivial symmetries has been profoundly advanced by the development of holographic symmetry algebras. This paper undertaken by Alfredo Guevara, Elizabeth Himwich, Monica Pate, and Andrew Strominger explores the intricate structure of these symmetries and their parametrization by generalized 2D currents, specifically within the celestial framework—a two-dimensional conformal field theory (CFT) representation of the four-dimensional scattering amplitudes.

Key Contributions

This paper presents a systematic construction of two infinite towers of 2D currents derived from positive-helicity particles—photons, gluons, and gravitons—that possess specified integral conformal weights. These currents are associated with an extensive range of conformally soft theorems, which map to symmetries on the celestial sphere. The researchers address the construction of these algebraic structures by deriving the commutation relations from the operator product expansion (OPE) coefficients' poles, unveiling a sophisticated closed subalgebra of the overall symmetry algebra.

A fundamental aspect of this work is the demonstration that standard 2D celestial CFT techniques can compute the properties of these symmetries and their algebra efficiently. This approach bypasses complicating factors associated with gauge choices and boundary conditions, offering a clearer view of the non-trivial symmetries in 4D gauge theories and gravity.

Theoretical and Practical Implications

1. Classification of Non-Trivial Symmetries: The structured classification of symmetries underscores a novel understanding of asymptotically flat spacetimes. While the Poincaré group symmetries have been known for their conservation laws, this paper expands on the BMS symmetry group by identifying additional non-trivial symmetries not encapsulated by traditional formulations.
2. Soft Theorems and Current Algebra: The infinite tower of symmetries reflects a parallel to an infinite tower of soft theorems. The derived current algebra reveals that leading, subleading, and—in the gravitational context—subsubleading symmetries generate the entirety of these towers. These findings suggest no new constraints arise for the S-matrix, implying that the algebraic structure elucidated here may survive quantum corrections and could persist in broader theoretical frameworks.
3. Celestial CFT Approach: The employment of celestial CFT offers a powerful toolkit for probing symmetries of gauge and gravitational forces. This method facilitates a deeper comprehension of celestial amplitudes and their role in scattering processes, potentially enriching the understanding of quantum gravity.
4. Assessment of General Dynamics: The paper offers a glimpse into the dynamics of gluons in Yang-Mills theory and gravitons in general relativity under the influence of these newly identified symmetries. By extending their methods to include quantum corrections and higher-order operators, the authors pave the way for future investigations into the far-reaching consequences of these symmetry structures.

Future Directions

The findings lead to several intriguing research directions:

• Complete Symmetry Algebra: With the current understanding forming only a subset of all possible symmetries, the quest for a comprehensive classification continues. This may include exploring the influence of shadow operators and emergent Goldstone bosons in dual gauge theories.
• Quantum Corrections: The paper provides the foundation for exploring how known algebras can adapt or extend when moving from classical to quantum domains and how quantum field theories' soft symmetry currents behave under higher-dimension operator influence.
• Expansion to Diverse Physical Models: Researchers are encouraged to apply these holographic methods to different physical models, such as those including IR confinement effects and other conditions that might affect gluon interactions.

In conclusion, this work represents a significant advancement in unraveling the symmetries of 4D gauge and gravitational theories by leveraging the celestial holographic framework. Such progress provides valuable insights into the foundational symmetries of nature and offers a robust platform for further exploring gravitational and quantum dynamics. The exploration and classification of these symmetry structures continue to challenge and refine the understanding of fundamental interactions in nature.