Flat Limit of AdS/CFT from the Perspective of AdS Geodesics: Constructing Scattering Amplitudes and Analyzing Antipodal Matching of Liénard-Wiechert Fields

Keskeiset käsitteet

This paper presents a novel geometric approach to understanding the flat limit of the AdS/CFT correspondence by analyzing the behavior of geodesics in AdS spacetime, demonstrating how this perspective provides insights into constructing flat space scattering amplitudes and explaining the antipodal matching of Liénard-Wiechert fields.

Tiivistelmä

• Bibliographic Information: Duary, S., & Upadhyay, S. (2024). Flat limit of AdS/CFT from AdS geodesics: scattering amplitudes and antipodal matching of Liénard-Wiechert fields. arXiv preprint arXiv:2411.08540.
• Research Objective: This paper aims to provide a new geometric perspective on the flat limit of the AdS/CFT correspondence by examining the role of geodesics in connecting the physics of AdS spacetime to flat spacetime observables.
• Methodology: The authors utilize the properties of null and timelike geodesics in AdS spacetime to derive expressions for scattering amplitudes in the flat limit. They further analyze the Liénard-Wiechert potentials in AdS, demonstrating how the antipodal matching of these fields in flat spacetime emerges from the AdS geometry.
• Key Findings: The authors demonstrate that the travel time of particles along geodesics in AdS can be used to directly obtain the creation and annihilation operators in the flat limit, simplifying the traditional approach of bulk operator reconstruction. They also show that the antipodal matching of Liénard-Wiechert fields observed in flat spacetime naturally arises from the global structure of AdS and its isometries.
• Main Conclusions: This work provides a more intuitive understanding of the flat limit of AdS/CFT by highlighting the crucial role of geodesic motion. It offers a novel method for calculating scattering amplitudes and sheds light on the emergence of flat spacetime properties, such as antipodal matching, from the AdS geometry.
• Significance: This research contributes to the ongoing effort to bridge the gap between our understanding of quantum gravity in AdS spacetime and its implications for flat spacetime physics. It offers valuable insights into the holographic encoding of flat space information within the AdS/CFT correspondence.
• Limitations and Future Research: The paper primarily focuses on massless and massive scalar fields. Exploring the extension of this geodesic approach to higher-spin fields and interacting theories would be a natural direction for future research. Additionally, investigating the implications of this geometric perspective for other aspects of flat space holography, such as asymptotic symmetries and soft theorems, could yield further insights.

Tilastot

Lainaukset

"The key takeaway is that flat space is a part of AdS space, meaning that the physics of flat space is inherently encoded in AdS spacetime."
"In the flat limit, the boundary correlation functions of certain operators should transform into S-matrix elements."
"Inspired by this, we propose a geometric approach to derive the formulas for creation and annihilation operators based on the geodesics of particles."
"We observe a parallel between the ℏ→0 limit in quantum mechanics and the flat limit."
"Strominger conjectured that data at past boundary of I+ should be antipodally matched to data at the future of past null infinity [43]."

Tärkeimmät oivallukset

Flat limit of AdS/CFT from AdS geodesics: scattering amplitudes and antipodal matching of Li\'enard-Wiechert fields

by Sarthak Duar... klo arxiv.org 11-14-2024

https://arxiv.org/pdf/2411.08540.pdf

Syvällisempiä Kysymyksiä

How can this geodesic-based approach be generalized to incorporate the effects of quantum corrections and stringy physics in the AdS/CFT correspondence?

This is a very interesting question that touches upon the frontiers of our understanding of the AdS/CFT correspondence. Here are some potential avenues for incorporating quantum corrections and stringy physics:

Quantum corrections to geodesics: Classical geodesics represent the dominant contribution in the large AdS radius limit. To incorporate quantum corrections, we need to consider the effects of quantum fluctuations around these classical paths. This can be achieved using the worldsheet theory of the corresponding string theory. In the AdS/CFT context, quantum corrections to scattering amplitudes would involve calculating stringy corrections to the worldsheet action and studying how they modify the geodesic picture.

Stringy states and extended objects: The geodesic approach primarily focuses on point-like particles. String theory introduces an infinite tower of massive states corresponding to different vibrational modes of strings. Additionally, it includes extended objects like D-branes. Incorporating these stringy objects would require going beyond the point-particle approximation and considering the dynamics of strings and branes in AdS spacetime. Their scattering amplitudes and interactions would involve more complex worldsheet topologies and boundary conditions.

Strong coupling and non-perturbative effects: The flat limit of AdS/CFT is often studied in the regime where the CFT is weakly coupled, corresponding to a large 't Hooft coupling in the dual string theory. However, to fully capture stringy physics, we need to understand the strongly coupled regime of the CFT. This might involve using non-perturbative techniques like integrability, localization, or numerical methods like lattice gauge theory.

Deformations of AdS and non-conformal CFTs: The AdS/CFT correspondence has been extended to include deformations of AdS spacetime, which are dual to non-conformal field theories. In these cases, the geodesic picture might need to be modified to account for the changing geometry of the bulk spacetime.
In summary, incorporating quantum corrections and stringy physics into the geodesic-based approach to the flat limit of AdS/CFT is a challenging but important problem. It requires a deeper understanding of the interplay between the worldsheet theory of strings, the dynamics of extended objects, and the strongly coupled regime of the CFT.

Could there be alternative geometric interpretations of the flat limit of AdS/CFT that provide different insights or computational advantages?

Yes, exploring alternative geometric interpretations of the flat limit of AdS/CFT is a promising direction for gaining new insights and computational tools. Here are a few possibilities:

Twistor space methods: Twistor theory offers a powerful geometric framework for describing massless particles and their interactions. It has been successfully applied to study scattering amplitudes in flat space Yang-Mills theory and gravity. Investigating the twistor space formulation of AdS/CFT and its flat limit could lead to new geometric interpretations of scattering amplitudes and potentially reveal hidden symmetries or structures.

Carrollian geometry: In the flat limit, the AdS boundary approaches a null hypersurface, which can be described using Carrollian geometry. This geometry is characterized by a degenerate metric and a different notion of causality compared to Lorentzian geometry. Studying the flat limit of AdS/CFT from the perspective of Carrollian geometry might provide new insights into the emergence of flat spacetime and its symmetries from the holographic duality.

Geometric quantization and coadjoint orbits: The AdS/CFT correspondence has connections to geometric quantization, where classical phase spaces are quantized using geometric structures. In this context, the flat limit could be related to the study of certain limits of coadjoint orbits of the conformal group. This approach might provide a more abstract and algebraic understanding of the flat limit and its relation to the representation theory of the conformal group.

Higher spin holography: Higher spin holography relates theories of interacting higher spin fields in AdS to vector models on the boundary. These theories exhibit enhanced symmetries and might offer a simpler setting to study the flat limit and its geometric interpretations. Exploring the flat limit of higher spin holography could provide valuable insights that could be generalized to more realistic string theory setups.
In conclusion, exploring alternative geometric interpretations of the flat limit of AdS/CFT is a rich area for future research. It has the potential to uncover new structures, symmetries, and computational techniques that could deepen our understanding of the holographic duality and its implications for quantum gravity in flat spacetime.

What are the implications of this geometric understanding of the flat limit for the emergence of spacetime itself from the holographic duality?

The geometric understanding of the flat limit of AdS/CFT offers intriguing hints about the emergence of spacetime from the holographic duality. Here are some key implications:

Spacetime as an emergent concept: The fact that flat spacetime can be obtained as a limit of AdS suggests that spacetime itself might not be a fundamental entity but rather an emergent concept arising from the underlying degrees of freedom of the CFT. In this picture, the geometry of spacetime would be encoded in the entanglement structure and correlations of the CFT degrees of freedom.

Holographic reconstruction of spacetime: The geodesic-based approach provides a concrete way to relate bulk points in AdS to boundary regions in the CFT. This supports the idea of holographic reconstruction, where the geometry of the bulk spacetime can be reconstructed from boundary data. Understanding how this reconstruction works in the flat limit could shed light on the emergence of locality and causality in quantum gravity.

Role of conformal symmetry: Conformal symmetry plays a crucial role in the AdS/CFT correspondence. In the flat limit, the conformal group contracts to the Poincaré group, which is the symmetry group of flat spacetime. This suggests that the emergence of spacetime symmetries is intimately connected to the structure of the conformal group and its representations.

Quantum entanglement and spacetime connectivity: The mapping between CFT regions and flat space regions, particularly the connection between Euclidean domes and timelike infinity, highlights the importance of quantum entanglement in understanding spacetime connectivity. The entanglement structure of the CFT could be responsible for "weaving" together different regions of spacetime in a way that is not manifest in the classical picture.

Beyond classical geometry: The appearance of complex points in the global time coordinate for massive particles suggests that the emergent spacetime might not be strictly classical. It could possess subtle quantum features and a more intricate geometry than what is captured by classical general relativity.
In conclusion, the geometric understanding of the flat limit of AdS/CFT provides compelling evidence for the emergence of spacetime from a holographic duality. It suggests that spacetime is not fundamental but rather arises from the entanglement and correlations of degrees of freedom living on a lower-dimensional boundary. Further exploration of this connection could lead to profound insights into the nature of quantum gravity and the emergence of spacetime itself.