Holographic Duality for Boundary Conformal Field Theory with T¯T Deformation: Exploring the Interplay of Boundary Effects and Deformation

Keskeiset käsitteet

This research paper proposes a holographic dual model for boundary conformal field theory (BCFT) with T¯T deformation, categorized into two types based on whether the boundary is deformed by the T¯T operator, and provides evidence for the duality by calculating entanglement entropy, boundary entropy, and energy spectrum.

Tiivistelmä

• Bibliographic Information: Deng, F., & Wang, Z. (2024). Holographic boundary conformal field theory with T¯T deformation. Journal of High Energy Physics. arXiv:2411.06345v1 [hep-th]

• Research Objective: This paper aims to investigate the holographic dual of boundary conformal field theories (BCFTs) with T¯T deformation, a question arising from the intersection of AdS/CFT correspondence, AdS/BCFT duality, and holographic T¯T CFTs.

• Methodology: The authors employ a bottom-up approach, combining the AdS/BCFT duality with the cutoff description of holographic T¯T CFT. They propose a bulk dual model consisting of AdS gravity enclosed by an EOW brane with Neumann boundary condition and a finite cutoff boundary with Dirichlet boundary condition. Two types of T¯T BCFTs are distinguished based on whether the boundary is deformed by the T¯T operator. To support their proposal, they calculate various quantities, including boundary entropy, energy spectrum for a finite interval, entanglement entropy, and Rényi entropy, comparing results from both field theory and gravity perspectives.

• Key Findings: The study reveals two distinct types of T¯T BCFTs with different holographic duals. For Type A (boundary-deformed), the boundary entropy serves as a measure of boundary deformation. Calculations of boundary entropy from disk partition function and holographic entanglement entropy show agreement. For Type B (boundary-undeformed), the boundary remains unaffected by the T¯T deformation. Calculations of entanglement entropy and Rényi entropy from both field theory and gravity perspectives also demonstrate consistency.

• Main Conclusions: The research proposes a novel holographic dual model for T¯T BCFT, providing evidence for its validity through calculations of key quantities. The distinction between boundary-deformed and boundary-undeformed cases highlights the nuanced interplay between boundary effects and T¯T deformation in holographic settings.

• Significance: This work advances the understanding of AdS/CFT correspondence in the context of BCFTs with T¯T deformation. It offers a new framework for studying strongly coupled CFTs with boundaries and sheds light on the holographic interpretation of T¯T deformation in such systems.

• Limitations and Future Research: The study primarily focuses on two specific examples of T¯T BCFTs. Exploring more general cases and extending the analysis to higher dimensions would provide further insights. Investigating other quantum information quantities, such as reflected entropy and entanglement negativity, could reveal additional aspects of this duality.

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Tärkeimmät oivallukset

Holographic boundary conformal field theory with $T\bar T$ deformation

by Feiyu Deng, ... klo arxiv.org 11-12-2024

https://arxiv.org/pdf/2411.06345.pdf

Syvällisempiä Kysymyksiä

How does the proposed holographic dual model for T¯T BCFT contribute to the broader understanding of quantum gravity and the AdS/CFT correspondence?

This paper proposes a novel holographic dual model for boundary conformal field theories (BCFTs) deformed by the T¯T operator, denoted as T¯T BCFTs. This model significantly contributes to our understanding of quantum gravity and the AdS/CFT correspondence in several ways:

Extending the AdS/CFT dictionary: The proposal enriches the AdS/CFT dictionary by incorporating the effect of T¯T deformations in the presence of boundaries. It provides a concrete gravitational description for T¯T BCFTs, associating them with AdS gravity enclosed by both an End-of-the-World (EOW) brane and a finite radial cutoff boundary. This connection allows for the exploration of strongly coupled T¯T BCFTs using the tools of classical gravity.

Classifying T¯T BCFTs: The research introduces a novel classification of T¯T BCFTs based on the behavior of the boundary under deformation. Type A T¯T BCFTs exhibit boundary deformation, quantified by changes in boundary entropy, while Type B T¯T BCFTs maintain an undeformed boundary. This distinction highlights the diverse ways in which T¯T deformations can impact a theory with a boundary, leading to distinct holographic realizations.

Probing quantum gravity: T¯T deformations are inherently non-local, providing a unique avenue to study the emergence of gravity from non-gravitational degrees of freedom. By studying the holographic duals of T¯T BCFTs, we gain insights into how non-locality in the boundary theory manifests in the bulk geometry, potentially shedding light on the nature of quantum gravity.

New tools for entanglement entropy: The paper demonstrates the calculation of entanglement entropy and Rényi entropy in T¯T BCFTs using both field-theoretic and holographic techniques. This not only provides further evidence for the proposed duality but also develops new tools for understanding entanglement in the presence of T¯T deformations, a topic of significant interest in quantum information theory and holography.
In essence, this research pushes the boundaries of the AdS/CFT correspondence by incorporating the complexities of T¯T deformations and boundaries. This leads to a deeper understanding of the interplay between geometry and quantum entanglement, potentially offering valuable insights into the nature of quantum gravity.

Could there be alternative holographic interpretations of T¯T deformed BCFTs that do not rely on the distinction between boundary-deformed and boundary-undeformed cases?

While the paper focuses on a specific holographic interpretation of T¯T deformed BCFTs based on the boundary deformation behavior, alternative interpretations might exist. Here are some possibilities:

Dynamical boundary conditions: Instead of classifying T¯T BCFTs into two distinct types, one could explore the possibility of describing both cases within a unified framework using dynamical boundary conditions on the cutoff surface. These boundary conditions could encode the response of the boundary degrees of freedom to the T¯T deformation, potentially capturing both deformed and undeformed boundary scenarios.

Non-trivial dilaton profiles: The T¯T deformation is known to be related to a flow in the space of string theory backgrounds. It's conceivable that alternative holographic duals could involve non-trivial profiles for the dilaton field in AdS, reflecting the changing string coupling under the T¯T flow. This could provide a more geometric understanding of the deformation without relying solely on the boundary behavior.

Higher-spin generalizations: T¯T deformations have intriguing connections to higher-spin theories of gravity. It's possible that alternative holographic duals could be formulated within the framework of higher-spin AdS/CFT, where the T¯T deformation might correspond to a specific deformation of the higher-spin symmetry algebra.

Non-geometric backgrounds: T¯T deformations are known to lead to non-local theories, suggesting that their holographic duals might involve non-geometric backgrounds in string theory. Exploring such exotic possibilities could provide a radically different perspective on the nature of T¯T deformations and their holographic interpretation.
It's important to note that these are speculative ideas, and further research is needed to determine their viability. Nevertheless, the existence of alternative holographic interpretations highlights the richness of the AdS/CFT correspondence and the potential for new discoveries in this field.

How can the insights gained from studying T¯T BCFTs be applied to other areas of theoretical physics, such as condensed matter physics or cosmology?

The study of T¯T BCFTs, while deeply rooted in string theory and quantum gravity, has the potential to offer valuable insights into other areas of theoretical physics:
Condensed Matter Physics:

Quantum Hall Effect: BCFTs have been employed to describe certain aspects of the quantum Hall effect, particularly edge states. T¯T deformations, with their connection to non-locality and strong coupling, could provide new theoretical tools to model and understand the intricate behavior of edge states in quantum Hall systems, especially in regimes where conventional approaches break down.

Topological Phases of Matter: The interplay between boundaries and topology is crucial in the study of topological phases of matter. T¯T deformations, by modifying the boundary conditions and potentially inducing topological transitions, could offer a novel way to explore and classify topological phases, leading to the discovery of new exotic states of matter.

Strongly Correlated Systems: T¯T deformations provide a controlled way to study strongly coupled theories. The insights gained from T¯T BCFTs could be applied to model strongly correlated condensed matter systems, such as high-temperature superconductors, where understanding the interplay between strong correlations and boundary effects is crucial.
Cosmology:

Holographic Cosmology: The AdS/CFT correspondence has inspired holographic models of cosmology, where the early universe is described by a dual gravitational theory. T¯T deformations, by modifying the UV behavior of the boundary theory, could be used to model the very early universe, potentially providing insights into inflation or other cosmological scenarios beyond the reach of standard approaches.

Entanglement and Cosmic Structures: Entanglement entropy plays a crucial role in understanding the formation of cosmic structures and the information paradox of black holes. The tools developed for studying entanglement in T¯T BCFTs could be adapted to cosmological settings, potentially shedding light on the role of entanglement in the evolution of the universe.

Quantum Gravity and Cosmology: Ultimately, a deeper understanding of T¯T deformations and their holographic duals could contribute to the development of a complete theory of quantum gravity. Such a theory is essential for understanding the very early universe, where quantum gravitational effects are expected to be significant.
In summary, the study of T¯T BCFTs, while motivated by fundamental questions in string theory and quantum gravity, has the potential to impact diverse areas of theoretical physics. By bridging the gap between abstract theoretical concepts and concrete physical phenomena, this research could lead to new discoveries and a deeper understanding of the universe we inhabit.