Torsion Alters Holographic Entanglement, Revealing New Links Between Gravity and Information

Scientists are increasingly exploring the connection between gravity, quantum entanglement, and information theory, and a new study sheds light on the role of torsion in these relationships. Dušan Đorđević and Dragoljub Gočanin, both from the Faculty of Physics at the University of Belgrade, present a novel prescription for incorporating torsion into calculations of holographic entanglement entropy within five-dimensional Chern-Simons gravity. Building upon the foundational work of Ryu and Takayanagi, this research significantly extends existing holographic entanglement entropy generalisations, which typically assume torsion-free spacetime. Their findings demonstrate that torsion generates a universal, logarithmically divergent term in the entanglement entropy, offering crucial insight into how geometric properties of spacetime influence quantum information and potentially refining our understanding of gravity’s holographic nature.

Researchers have uncovered a novel connection between torsion, a twisting of spacetime, and entanglement entropy, a fundamental measure of quantum connectedness. This work demonstrates that torsion within a five-dimensional Chern-Simons gravity theory induces a unique, logarithmically divergent term in the entanglement entropy of its four-dimensional holographic dual. The discovery offers a new pathway for understanding how geometric properties in higher-dimensional spaces influence quantum information on their boundaries, potentially reshaping our understanding of quantum gravity. This study introduces a prescription for incorporating torsion into calculations of holographic entanglement entropy, building upon the established Ryu-Takayanagi framework which relates entanglement to the geometry of spacetime. The team’s calculations reveal that torsion generates a universal divergent term in the entanglement entropy, scaling proportionally to the logarithm of the ultraviolet cutoff, a standard regulator used in quantum field theory to handle infinities. By demonstrating that torsion directly contributes to entanglement entropy, the research opens new avenues for exploring the role of non-Riemannian geometry in holographic systems. This is particularly relevant in condensed matter physics, where torsion may provide an effective description of spin-transport phenomena and contribute to understanding holographic conductivity. Furthermore, the work builds upon existing holographic methods and Wald’s formula for black hole entropy in Chern-Simons gravity, providing a consistent framework for incorporating torsion into holographic calculations. The researchers propose that this approach could be extended to explore more complex scenarios, potentially leading to a deeper understanding of the interplay between gravity, quantum information, and the fundamental nature of spacetime itself. A detailed examination of five-dimensional Chern-Simons gravity forms the basis of this work, specifically focusing on its application to holographic entanglement entropy. The research begins with a particular solution, AdS5 space with axial torsion, and proposes a method for incorporating torsion into calculations of entanglement entropy for its four-dimensional holographic dual. This approach leverages the first-order formulation of gravity, treating both affine (parallelism) and metric structures as independent entities; dynamical variables consist of the vielbein, representing a local frame field, and the spin connection, acting as the gauge field for local Lorentz transformations. Curvature and torsion are defined as mathematical forms derived from the spin connection and vielbein, allowing for a precise characterisation of the spacetime geometry. The choice of a first-order formalism is advantageous as it naturally accommodates torsion, unlike traditional Riemannian approaches which implicitly assume a torsion-free spacetime. To compute entanglement entropy, the study employs gravitational Wilson lines, extending a previously established result linking these lines to the relevant RT surfaces. The path of this Wilson line is determined by a geodesic equation defined in terms of the vielbein and spin connection, effectively tracing the minimal surface in the bulk spacetime. The research builds upon existing work in three-dimensional Chern-Simons gravity and Lovelock theory, adapting these concepts to the five-dimensional context. The Mielke-Baekler model, a specific instance of three-dimensional gravity with an explicit torsional term, provides a crucial theoretical foundation. This model’s action incorporates a translational Chern-Simons term, directly involving torsion, and allows for a non-Riemannian, torsion-full spacetime solution. By analysing the behaviour of the spin connection and its relation to the Riemannian component, the study suggests that the generalisation of the Ryu-Takayanagi proposal can be achieved relatively straightforwardly, even in the presence of torsion. Calculations reveal a universal, torsion-induced logarithmic divergence in the entanglement entropy of a four-dimensional conformal field theory. This divergent term arises solely from the presence of torsion within the five-dimensional Chern-Simons gravity setting, and its magnitude is proportional to the logarithm of the ultraviolet cutoff. The research establishes a holographic connection between bulk torsion and boundary entanglement entropy, demonstrating that this divergence is a fundamental consequence of the geometry. Specifically, the study considers a solution of five-dimensional Chern-Simons gravity, AdS5 space with axial torsion, and proposes a method for incorporating torsion into the computation of entanglement entropy for its holographic dual. The analysis builds upon previous work in Riemannian Lovelock theory and Wald’s formula for black hole entropy in Chern-Simons gravity with torsion. The resulting holographic reproduction of the four-dimensional conformal field theory’s entanglement entropy confirms the predicted logarithmic divergence. In the Mielke-Baekler model, the boundary theory possesses two equal central charges, (c_R = c_L = 24\pi k l), defined on a Riemannian manifold. Consequently, the entanglement entropy takes the standard conformal field theory form: (SEE = \frac{3}{2} G_N \frac{1}{1-3\alpha^2} \frac{1}{2} \ln \frac{L}{\epsilon}), where (k = \frac{1}{16\pi G_N}) and (L) is a characteristic length scale. The entropy of the BTZ black hole within this model remains unaffected by torsion, with the parameter (\alpha) influencing the entropy formula only through the effective AdS radius. Furthermore, analysis of a five-dimensional Chern-Simons gravity black hole solution, specifically, AdS5 with axial torsion and a flat three-manifold, reveals non-vanishing boundary torsion. The strength of this torsion is quantified by the parameter (C), appearing in the torsion tensor (T_i = -C r \epsilon_{ijk}e_j \wedge e_k), and influences the holographic dual’s entanglement entropy. The use of the Fefferman-Graham expansion demonstrates how bulk torsion induces a corresponding boundary torsion, establishing a direct link between the gravitational and field theory descriptions. Scientists have long sought a complete description of gravity that seamlessly integrates with quantum mechanics, and this work represents a subtle yet significant step towards that goal. The holographic principle, linking gravity in higher dimensions to quantum field theories in lower ones, provides a powerful framework for exploring this connection, but its application to complex scenarios has proven challenging. Most holographic calculations assume a simplified, torsion-free geometry, ignoring a property of spacetime that could be crucial in more realistic settings. This research addresses that omission by developing a method to incorporate torsion into calculations of holographic entanglement entropy. The implications extend beyond purely theoretical considerations; entanglement entropy is a measure of quantum connectedness, and understanding its behaviour in gravitational systems could shed light on the emergence of spacetime itself. Moreover, the discovery of a universal divergent term generated solely by torsion offers a new diagnostic tool for identifying and characterising these effects in both theoretical models and potentially in future observations of extreme gravitational environments. However, the calculations are performed within a specific theoretical framework, five-dimensional Chern-Simons gravity, and extending the results to more general spacetimes and gravitational theories will be a considerable undertaking. The precise physical interpretation of the divergent term also requires further investigation. Nevertheless, by opening up the possibility of studying torsion holographically, this work paves the way for a deeper understanding of quantum gravity and its connection to the fundamental structure of reality, potentially influencing future research into black hole physics and the very fabric of spacetime.