Entanglement Entropy Advances Understanding of Root-Deformed AdS/CFT in Three-Dimensional Space

The behaviour of entanglement within deformed anti-de Sitter (AdS) / conformal field theory (CFT) correspondence is a central problem in theoretical physics, with implications for understanding quantum gravity and strongly coupled systems. Saikat Biswas of the Indian Institute of Technology Kanpur, along with co-authors, investigate how introducing both λ and root deformations impacts reflected and entanglement entropy. Their work employs a mixed boundary condition framework to analyse modifications to entanglement structures within three-dimensional AdS space. This research is significant because it provides insights into the relationship between solvable irrelevant deformations and associated -theoretic quantities, ultimately illuminating the entanglement structure of deformed conformal field theories.

Entanglement Entropy Under AdS/CFT Deformations

Scientists demonstrate a novel investigation into the effects of T T and root-T T deformations on entanglement entropy, examining both pure and mixed state entanglement measures within the framework of the AdS/CFT correspondence. The research utilizes a mixed boundary condition framework to analyse how these deformations alter entanglement structures in three-dimensional AdS space, providing new insights into the relationship between solvable irrelevant deformations and quantum information-theoretic quantities. This work establishes a connection between theoretical constructs and the entanglement structure of deformed conformal field theories, furthering understanding of quantum gravity and strongly coupled systems. The study unveils how the T T and root-T T deformations impact entanglement wedge cross sections (EWCS), a crucial quantity related to reflected entropy, which characterizes correlations in mixed quantum states.

Researchers meticulously computed corrections to the EWCS using the mixed boundary condition approach, comparing these results with existing data obtained from the AdS cutoff prescription and direct calculations within the conformal field theory. This comparison serves as a rigorous test of the mixed boundary condition framework’s validity when applied to mixed-state entanglement measures, confirming its consistency and broadening its applicability. Experiments show that the team explored various configurations, including two disjoint intervals, two adjacent intervals, and a single interval, under both vanishing and finite chemical potential conditions to comprehensively assess the impact of the deformations. The analysis extends to finite temperature scenarios, further refining the understanding of entanglement behaviour in these deformed conformal field theories with and without conserved charges.

This detailed examination of different configurations and conditions allows for a nuanced understanding of how the deformations modify entanglement properties. The research establishes a robust holographic framework for studying entanglement in deformed theories, building upon previous work that successfully reproduced pure-state entanglement entropy using the mixed boundary condition approach. This work opens avenues for exploring more complex entanglement measures and their geometric interpretations, potentially leading to a deeper understanding of quantum correlations in strongly coupled systems and the emergence of spacetime geometry. The findings have implications for theoretical advancements in quantum information theory and the holographic principle, offering a pathway to explore the interplay between quantum entanglement and gravity.

Entanglement and Reflected Entropy under AdS Deformations

The study investigates the impact of both T T and root-T T deformations on entanglement entropy and reflected entropy within three-dimensional Anti-de Sitter (AdS) space, examining both pure and mixed quantum states. Researchers employed a mixed boundary condition framework to analyse how these deformations alter entanglement structures, focusing on their implications for theoretical quantities. This approach allowed for a detailed examination of solvable irrelevant deformations and their connection to entanglement characteristics. Scientists developed a methodology to compute corrections to the entanglement wedge cross section, a holographic representation of reflected entropy, and rigorously compared these results with those derived from the AdS cutoff prescription and existing conformal field theory calculations.

This comparison served as a crucial validation of the mixed boundary condition framework when applied to mixed-state entanglement measures, confirming its reliability beyond pure-state analysis. The team engineered calculations within T T-deformed BTZ and rotating BTZ geometries, utilising the mixed boundary condition to determine first-order corrections to the entanglement wedge cross section. Further innovation involved extending this framework to the root-T T deformation, an unconventional irrelevant deformation of two-dimensional quantum field theories. The research pioneered the application of the mixed boundary condition description to this more complex scenario, testing the robustness and adaptability of the method across a wider range of deformed AdS/CFT configurations.

Calculations involved deriving a correction formula for n-sheeted manifolds using the partition function for a single interval on the field theory side, subsequently computing geodesic lengths within the deformed geometry. The resulting first-order corrections consistently matched field theory predictions, demonstrating the power of the holographic approach and solidifying the mixed boundary condition as a versatile tool for probing entanglement in deformed conformal field theories. This work establishes a strong link between geometric calculations in the bulk AdS space and field theory results, providing new insights into the nature of quantum correlations in deformed systems and validating the holographic duality.

Deformations Alter Entanglement Entropy in AdS Space

Scientists investigated the effects of ‘T T’ and ‘root-T T’ deformations on reflected and entanglement entropy within both pure and mixed state entanglement measures. The research utilizes a mixed boundary condition framework to analyse how these deformations alter entanglement structures, exploring their implications within three-dimensional AdS space. Results illuminate the interplay between solvable irrelevant deformations and quantum information-theoretic quantities, providing insight into the entanglement structure of deformed conformal field theories. This work builds upon the AdS/CFT correspondence, linking boundary conformal field theories to dual gravitational theories in asymptotically AdS spacetime.

Experiments revealed that reflected entropy, a measure of quantum correlations in mixed states, can be constructed using replica methods in CFT2. Holographic calculations demonstrate that reflected entropy equates to twice the entanglement wedge cross section in AdS3, offering a geometric method for characterizing correlations in mixed states. The team measured the impact of the ‘T T’ deformation, an irrelevant deformation generated by the determinant of the stress-energy tensor, on entanglement measures for both pure and mixed states. Despite its irrelevance, the deformed theory remains remarkably solvable, admitting exact energy spectra and partition functions while preserving integrability.

Further analysis focused on the ‘root-T T’ deformation, a non-analytic operator generating a flow distinct from the standard ‘T T’ deformation. Measurements confirm that this deformation also impacts entanglement, revealing a rich integrable framework. The study employed Dirichlet-Neumann mixed boundary conditions to provide a complementary view to existing holographic proposals, allowing for the investigation of corrections to pure-state entanglement. Data shows that these deformations modify entanglement structures in predictable ways, offering a deeper understanding of quantum field-theoretic phenomena through a geometric lens.

The research delivers a detailed exploration of entanglement entropy and its holographic dual in ‘root-T T’ deformed CFTs, considering both vanishing and finite chemical potential scenarios. Tests prove that the framework can be extended to finite temperatures and conserved charges, further solidifying its applicability to a wider range of physical systems. Measurements confirm the validity of the Quantum Information Neutrality Condition (QNEC) in both ‘T T’ and ‘root-T T’ deformed theories, validating the consistency of the holographic description and providing a powerful tool for studying quantum correlations.

Entanglement Entropy Under Deformations in CFT

This research investigates the effects of both T-T and root-T-T deformations on entanglement entropy and related measures within two-dimensional conformal field theories. Through a mixed boundary condition framework applied to three-dimensional Anti-de Sitter space, the study details how these deformations alter the structure of entanglement, offering insights into the relationship between solvable irrelevant deformations and theoretical quantities describing entanglement. The findings demonstrate a connection between these deformations and the entanglement wedge cross section, providing a geometric interpretation of correlations in mixed quantum states. The work extends previous investigations of T-T deformations to include the root-T-T deformation, analysing its impact on quantities like reflected entropy and the Quantum Entanglement Criterion (QNEC). Authors acknowledge limitations inherent in the approximations used within the holographic duality, specifically concerning the finite radial cutoff employed in the bulk gravitational description. Future research could explore the behaviour of these deformations in more complex scenarios, potentially extending the analysis to higher-dimensional conformal field theories or investigating the implications for black hole physics and quantum gravity.