A Comment on Boundary Correlators: Soft Omissions and the Massless S-Matrix (Original Title)

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This paper highlights a typically overlooked soft contribution in the extrapolate dictionary for massless scattering in flat spacetime, demonstrating its significance in understanding the relationship between celestial amplitudes, Carrollian CFTs, and bulk scattering dynamics.

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Bibliographic Information:

Jørstad, E., & Pasterski, S. (2024). A Comment on Boundary Correlators: Soft Omissions and the Massless S-Matrix. arXiv preprint arXiv:2410.20296.

Research Objective:

This paper investigates the extrapolate dictionary for massless particles in flat spacetime, aiming to address inconsistencies between conventional approaches to celestial holography and the expected behavior of extrapolated bulk correlation functions.

Methodology:

The authors revisit the saddle point approximation used to derive the extrapolate dictionary, carefully analyzing the large-r limit of bulk correlation functions in flat-Bondi coordinates. They then compare the corrected extrapolate dictionary to the electric and magnetic branch Carrollian correlators.

Key Findings:

• The conventional saddle point approximation omits a soft, zero-energy term that is crucial for consistency with extrapolated bulk correlation functions.
• This omission explains the discrepancy between the distributional nature of celestial amplitudes and the analytic behavior of certain extrapolated bulk correlators.
• The corrected extrapolate dictionary reveals that boundary correlators are a combination of electric and magnetic branch Carrollian correlators.
• Despite their time-independence, magnetic branch correlators, often overlooked in scattering amplitude calculations, can encode significant information about the dynamics of the bulk theory.

Main Conclusions:

• The corrected extrapolate dictionary provides a more complete understanding of the relationship between bulk scattering and boundary correlators in celestial holography.
• The inclusion of soft terms and the recognition of magnetic branch contributions are essential for accurately capturing the dynamics of the bulk theory.
• The results bridge the gap between celestial amplitudes, Carrollian CFTs, and recent work on flat space dictionaries and shadow celestial amplitudes.

Significance:

This work refines the understanding of celestial holography by highlighting the importance of previously overlooked soft contributions and their connection to different branches of Carrollian CFTs. This has implications for extracting bulk dynamics from boundary correlators and provides new insights into the relationship between celestial amplitudes and shadow transforms.

Limitations and Future Research:

The paper primarily focuses on massless scalar fields in four spacetime dimensions. Further research could explore the generalization of these findings to include massive and spinning particles, gauge theories, and higher dimensions. Investigating the cancellation of multiple soft insertions and establishing a more concrete connection to 3D shadow transforms are also promising avenues for future work.

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A Comment on Boundary Correlators: Soft Omissions and the Massless S-Matrix

by Eivi... : arxiv.org 10-29-2024

https://arxiv.org/pdf/2410.20296.pdf

Mélyebb kérdések

How might the inclusion of gravitational degrees of freedom and their associated soft theorems affect the analysis of soft contributions in the extrapolate dictionary?

Including gravitational degrees of freedom and their associated soft theorems would significantly enrich the analysis of soft contributions in the extrapolate dictionary in the following ways:

Modification of Soft Terms: The presence of gravitons introduces new soft modes governed by the Weinberg soft graviton theorem. These soft graviton contributions would modify the soft term in the corrected extrapolate dictionary (Equation 2.11 in the paper). Instead of just a term involving ωa(ω, z′, ¯z′)|ω=0, we would expect additional terms capturing the soft graviton insertions.

Ward Identities and Gauge Invariance: The soft graviton theorem is intimately tied to BMS symmetry, the asymptotic symmetry group of asymptotically flat spacetimes. The corrected extrapolate dictionary, including gravitons, would need to respect these symmetries. This implies that the Ward identities associated with BMS transformations would impose constraints on the form of the soft terms, ensuring gauge invariance.

Gravitational Dressing of Operators: Gravitons couple universally to all forms of energy, including the massless scalar field considered in the paper. This implies that the extrapolated operators themselves would be "gravitationally dressed." This dressing would likely involve a resummation of soft graviton contributions, potentially leading to non-trivial modifications of the operator product expansions (OPEs) and correlation functions.

Memory Effects and Infrared Structure: Soft graviton theorems are deeply connected to gravitational memory effects, which are permanent shifts in the relative positions of detectors caused by the passage of gravitational waves. The inclusion of soft graviton contributions in the extrapolate dictionary could provide insights into how these memory effects are encoded in the celestial CFT. Moreover, it could shed light on the infrared structure of gravity in asymptotically flat spacetimes.

Beyond the 4-Point Function: While the paper focuses on the 4-point function, the inclusion of gravitons becomes particularly interesting for higher-point correlation functions. The interplay between soft graviton theorems and the celestial basis could lead to novel ways of organizing and computing scattering amplitudes in quantum gravity.

In summary, incorporating gravitational degrees of freedom and their associated soft theorems would not only modify the specific form of the corrected extrapolate dictionary but also deepen our understanding of the infrared structure of gravity, its symmetries, and its connection to celestial holography.

Could there be alternative formulations of celestial holography that circumvent the need for explicitly considering separate electric and magnetic branches of Carrollian CFTs?

While the current formulation of celestial holography relies on distinguishing between electric and magnetic branches of Carrollian CFTs, exploring alternative formulations that might circumvent this separation is an intriguing prospect. Here are some speculative ideas:

Unified Description via Deformation: One possibility is to seek a "parent" Carrollian CFT that encompasses both electric and magnetic branches as different sectors or limits. This parent CFT could potentially be deformed by relevant operators, with the electric and magnetic branches arising as different fixed points of the renormalization group flow.

Higher-Dimensional Embedding: Another avenue is to embed the 4D asymptotically flat spacetime into a higher-dimensional ambient space. This embedding could potentially lead to a more unified description of the boundary CFT, where the electric and magnetic branches emerge as different projections or restrictions of a single higher-dimensional theory.

Twistor Space Formalism: Twistor theory provides a powerful framework for describing massless fields and scattering amplitudes. It might be possible to formulate celestial holography directly in twistor space, where the distinction between electric and magnetic branches could be more naturally incorporated or even dissolved.

Non-local Operators and Extended Symmetries: The separation into electric and magnetic branches arises partly from the local nature of the operators considered. Introducing non-local operators or exploring extended symmetry algebras beyond the standard Poincaré and BMS groups might offer a way to bridge the gap between the two branches.

Alternative Boundary Structures: Instead of focusing solely on null infinity, exploring alternative boundary structures, such as spatial infinity or the future/past boundary of spacetime, could provide new perspectives on celestial holography. These alternative boundaries might admit CFT descriptions that naturally incorporate both electric and magnetic degrees of freedom.

It's important to note that these are speculative ideas, and it remains an open question whether such alternative formulations exist and, if so, whether they would offer significant advantages over the current framework. Nevertheless, exploring these possibilities could lead to a deeper understanding of celestial holography and its potential to unravel the mysteries of quantum gravity in asymptotically flat spacetimes.

What are the implications of the connection between magnetic branch correlators and bulk dynamics for understanding quantum gravity in asymptotically flat spacetimes?

The connection between magnetic branch correlators and bulk dynamics, as highlighted in the paper, has profound implications for our understanding of quantum gravity in asymptotically flat spacetimes:

Holographic Reconstruction of Bulk Physics: The fact that magnetic branch correlators, despite their time-independence at the boundary, can encode information about the analytic structure of bulk correlation functions suggests a remarkable holographic principle at work. It implies that the celestial CFT, even when restricted to the magnetic branch, contains enough information to reconstruct aspects of the bulk dynamics.

New Observables for Quantum Gravity: Magnetic branch correlators, being non-distributional on the celestial sphere, offer a new set of observables for quantum gravity in asymptotically flat spacetimes. Unlike scattering amplitudes, which are inherently tied to asymptotic states and the S-matrix, these correlators provide a way to probe the bulk dynamics in a more direct and potentially more fundamental way.

Insights into the Soft Sector: The connection between magnetic branch correlators and the soft sector of the theory, as evidenced by their relation to shadow transforms and soft limits of amplitudes, suggests a deep interplay between these two seemingly disparate aspects of quantum gravity. This interplay could hold the key to understanding the infrared structure of gravity and its role in celestial holography.

Constraints on Quantum Gravity Theories: The specific form of the magnetic branch correlators and their connection to bulk dynamics could impose non-trivial constraints on viable theories of quantum gravity. By studying these correlators in various candidate theories, we can gain insights into their consistency and potential to describe the real world.

Bridge to Cosmology: Asymptotically flat spacetimes serve as idealized models for isolated systems in gravity. However, our universe is inherently cosmological. The insights gained from studying magnetic branch correlators in flat spacetimes could provide valuable hints for developing a holographic description of cosmology, potentially shedding light on the early universe and the nature of dark energy.

In conclusion, the connection between magnetic branch correlators and bulk dynamics opens up exciting new avenues for exploring quantum gravity in asymptotically flat spacetimes. It suggests a richer and more intricate holographic dictionary than previously anticipated, with the potential to revolutionize our understanding of the fundamental nature of gravity and its interplay with quantum mechanics.