Computing Non-planar Corrections to Operator Dimensions in ABJM Theory Using Quantum M2 Branes

Основні поняття

This paper proposes a novel method to compute non-planar corrections to operator dimensions in ABJM theory at strong coupling by leveraging the theory's duality to M-theory and employing semiclassical quantization of M2 branes wrapped on an internal circle in AdS4 × S7/Zk.

Анотація

Bibliographic Information:

Giombi, S., Kurlyand, S. A., & Tseytlin, A. A. (2024). Non-planar corrections in ABJM theory from quantum M2 branes. arXiv preprint arXiv:2408.10070v3.

Research Objective:

This research aims to develop a method for calculating non-planar corrections to the scaling dimensions of operators in ABJM theory at strong coupling, a problem that has been challenging to address using traditional string theory techniques.

Methodology:

The authors utilize the AdS/CFT correspondence, specifically the duality between ABJM theory and M-theory on AdS4 × S7/Zk. They propose that the non-planar corrections can be captured by semiclassically quantizing M2 branes wrapped around the 11d circle in the S7/Zk geometry. This approach is analogous to the semiclassical quantization of strings in AdS spacetimes for calculating planar contributions but extends the analysis to include string loop corrections through the M-theory perspective.

Key Findings:

• The authors demonstrate that the semiclassical M2 brane quantization method correctly reproduces the known structure of non-planar corrections in the 1/N expansion of the ABJM theory.
• They apply this method to compute the leading non-planar correction to the cusp anomalous dimension at strong coupling, finding it scales as λ²/N².
• The method is further applied to calculate the leading non-planar corrections to the dimensions of operators dual to "short" and "long" circular strings with two equal angular momenta in CP3.

Main Conclusions:

The research presents a powerful new approach to studying non-planar corrections in ABJM theory at strong coupling. By utilizing the M-theory perspective and semiclassical M2 brane quantization, the authors can access information about string loop corrections that are difficult to compute directly. This method provides valuable insights into the non-planar sector of the AdS/CFT correspondence and opens avenues for further exploration of non-planar effects in ABJM and related theories.

Significance:

This work significantly contributes to the understanding of the non-planar sector of the AdS/CFT correspondence, which has been a challenging area of research. The proposed method offers a new way to study non-planar effects at strong coupling, providing insights into the quantum nature of the duality.

Limitations and Future Research:

• The current work focuses on the leading non-planar corrections. Extending the analysis to higher-order corrections would require considering higher-loop contributions in the M2 brane quantization, which could be technically challenging.
• Exploring the applicability of this method to other observables in ABJM theory and other examples of the AdS/CFT correspondence would be an interesting avenue for future research.

Статистика

The leading non-planar correction to the cusp anomalous dimension at strong coupling scales as λ²/N².
The M2 brane tension scales as T² ~ √(kN).
The string coupling constant is related to the parameters of the ABJM theory as g_s ~ √π (2λ)^(5/4)/N.
The effective string tension is given by T = √(λ)/(2√π).

Цитати

Ключові висновки, отримані з

Non-planar corrections in ABJM theory from quantum M2 branes

by Simone Giomb... о arxiv.org 11-06-2024

https://arxiv.org/pdf/2408.10070.pdf

Глибші Запити

How does this method for calculating non-planar corrections compare to other approaches, such as those based on integrability or localization techniques?

This method, based on the semiclassical quantization of M2 branes in AdS4 × S7/Zk, offers a distinct approach to calculating non-planar corrections in ABJM theory compared to integrability or localization techniques. Here's a comparative analysis:
Semiclassical M2 brane quantization:

Strengths:

Strong coupling regime: Particularly well-suited for investigating the strong-coupling behavior of non-planar corrections, a regime where integrability and localization techniques often face challenges.
Captures all-genus contributions: A single M2 brane computation effectively encapsulates information from all string loop orders due to the dependence on the 11d background parameter 'k', which is related to the string coupling.

Limitations:

Limited to specific observables: Primarily applicable to observables that have well-defined dual descriptions in terms of semiclassical M2 brane configurations.
Technically challenging: Involves intricate calculations in the context of the M2 brane action, which is formally non-renormalizable.
Integrability:

Strengths:

Exact results in the planar limit: Enables the computation of certain observables, like anomalous dimensions, exactly in the planar limit ('t Hooft coupling expansion).
Applicable at various coupling strengths: Can potentially provide insights into both weak and strong coupling regimes.

Limitations:

Non-planar corrections are difficult: Extending integrability techniques to incorporate non-planar corrections remains a formidable challenge.
Limited set of observables: Not all observables are amenable to integrability-based calculations.
Localization:

Strengths:

Exact results for specific observables: Allows for the exact computation of a select set of supersymmetric observables.
Non-perturbative insights: Can provide access to non-perturbative effects in certain cases.

Limitations:

Restricted to supersymmetric observables: Not applicable to non-supersymmetric observables like the cusp anomalous dimension.
Limited applicability to non-planar corrections: Extending localization techniques to handle non-planar corrections is generally non-trivial.
In summary:
The semiclassical M2 brane quantization method provides a valuable tool for studying non-planar corrections at strong coupling, complementing integrability and localization techniques. Each approach has its strengths and limitations, and the most suitable method depends on the specific observable and the regime of interest.

Could the presence of non-perturbative effects in M-theory, such as M-instantons, modify the results obtained from the semiclassical M2 brane quantization?

Yes, the presence of non-perturbative effects in M-theory, such as M-instantons, could potentially modify the results obtained from the semiclassical M2 brane quantization.

M-instantons and the semiclassical expansion: The semiclassical M2 brane expansion, as presented in the context, primarily focuses on perturbative corrections around a classical M2 brane configuration. It assumes that the dominant contributions come from these perturbative fluctuations. However, M-instantons, being non-perturbative objects, could introduce additional contributions that are not captured by this expansion.

Potential modifications: M-instantons could lead to the following modifications:

Exponentially suppressed corrections: They might contribute exponentially suppressed terms in the 1/N expansion, potentially modifying the subleading terms in the strong coupling expansion of observables like the cusp anomalous dimension.
New saddle points: In certain cases, M-instantons could even give rise to new saddle points in the M2 brane path integral, leading to qualitatively different results compared to the perturbative analysis.

Dependence on specific configurations: The extent to which M-instantons affect the semiclassical results depends on the specific M2 brane configuration and the observable under consideration. For instance, if the M2 brane worldvolume wraps a cycle that can support M-instanton configurations, their contributions might be more significant.
In conclusion:
While the semiclassical M2 brane quantization provides valuable insights into non-planar corrections, it's crucial to acknowledge that non-perturbative effects like M-instantons could potentially modify the results. Investigating the role of such non-perturbative effects is an important avenue for further research.

What are the implications of these findings for understanding the quantum nature of gravity in the context of the AdS/CFT correspondence?

The findings related to calculating non-planar corrections using semiclassical M2 brane quantization in the context of AdS4/CFT3 have profound implications for understanding the quantum nature of gravity through the lens of the AdS/CFT correspondence:

Beyond classical gravity: The ability to compute non-planar corrections, which correspond to string loop corrections on the AdS side, signifies a step beyond the classical description of gravity. It provides a window into the quantum effects of gravity, albeit in the specific setting of the AdS/CFT duality.

Emergence of spacetime from gauge theory: The fact that the large N expansion of the ABJM gauge theory, including non-planar corrections, can be captured by the semiclassical quantization of M2 branes suggests a deep connection between the degrees of freedom of the gauge theory and the quantum nature of spacetime in the dual theory. This supports the holographic principle, where the information about the quantum gravity theory is encoded in the lower-dimensional gauge theory.

Testing the AdS/CFT correspondence: The agreement between the strong coupling predictions from the M2 brane quantization and the expected structure of non-planar corrections in the ABJM theory provides further evidence for the validity of the AdS/CFT correspondence. It strengthens the link between gauge theories and quantum gravity, offering a testing ground for exploring quantum gravity in a controlled setting.

Towards M-theory understanding: The success of the M2 brane approach highlights the importance of M-theory as a framework for understanding quantum gravity. It suggests that M-theory might provide a more complete and consistent description of quantum gravity compared to perturbative string theory, particularly in the presence of non-perturbative effects.
In essence:
These findings contribute to the broader endeavor of unraveling the mysteries of quantum gravity by leveraging the powerful tools of the AdS/CFT correspondence. They provide compelling evidence for the interconnectedness of gauge theories and gravity, offering a glimpse into the quantum nature of spacetime and the potential role of M-theory in its description.