Dynamic Boundary Conditions Link Quantum Gravity to One-Dimensional Fluid Dynamics

The fundamental nature of black hole entropy, and how it arises from the microscopic arrangement of its constituent parts, remains a central question in theoretical physics. Suvankar Dutta, Shruti Menon, and Aayush Srivastav, from the Indian Institute of Science Education and Research, investigate this problem by exploring a novel connection between three-dimensional gravity and the behaviour of one-dimensional fluids. Their work demonstrates how a microscopic description of black hole states can emerge from a system of relativistic fermions, quantified using a mathematical technique called bosonization, and reveals a precise, one-loop calculation of the subtle logarithmic corrections to black hole entropy. This research is significant because it provides a new framework for understanding the quantum structure of black holes and suggests a universal origin for these corrections, independent of the specific details of the boundary conditions used in the calculation.ensure t

BTZ Black Holes and Conformal Field Theory

Researchers study three-dimensional gravity with a negative cosmological constant, investigating its connection to two-dimensional conformal field theory through the AdS/CFT correspondence. This duality offers a powerful framework for understanding quantum gravity, allowing scientists to calculate gravitational phenomena using the more manageable tools of quantum field theory. A central focus lies on the BTZ black hole, a three-dimensional black hole solution that serves as a crucial testing ground for this correspondence, and its microscopic entropy. Current calculations of the BTZ black hole’s entropy, based on conformal field theory, exhibit a logarithmic correction, a deviation from the Bekenstein-Hawking area law predicted by general relativity.

Investigating this logarithmic correction is crucial for validating the AdS/CFT correspondence and gaining deeper insights into the quantum nature of black holes. This work explores the relationship between bosonization, a technique for mapping fermionic systems to bosonic ones, and the counting of microstates for the BTZ black hole. By carefully analysing the microstate counting using bosonization techniques, the research seeks to determine whether the logarithmic correction is a genuine quantum effect or an artefact of the approximations used in the calculations. The research establishes a framework based on dynamic boundary conditions, where chemical potentials are not pre-defined but determined by the system itself. A boundary Hamiltonian, inspired by collective field theory, reduces the boundary dynamics to those of a one-dimensional fluid on a circle, with configurations corresponding to bulk geometries such as BTZ black holes. The system undergoes quantization via bosonization of relativistic fermions, yielding a microscopic description of black hole states in terms of Young diagrams, whose degeneracies match the predicted Bekenstein-Hawking entropy.

Two-Dimensional Yang-Mills Theory and String Theory Connections

This body of work encompasses a wide range of references related to research in areas like two-dimensional quantum field theory, specifically 2D Yang-Mills theory and its connection to string theory, as well as related topics like bosonization. The references demonstrate a strong focus on understanding the deep connections between these areas. A significant portion of the bibliography centers around the study of 2D Yang-Mills theory, its properties, and its relationship to string theory. This approach offers a non-perturbative way to understand quantum chromodynamics. The technique of bosonization is a recurring theme, suggesting its importance in analysing two-dimensional systems.

Many references deal with the large N limit of gauge theories, which simplifies calculations and reveals connections to string theory. There is a strong interest in logarithmic corrections to black hole entropy, which are often associated with quantum effects and the microstate counting of black holes. The inclusion of resurgence theory suggests an attempt to go beyond perturbative calculations and understand non-perturbative phenomena. The AdS/CFT correspondence is also mentioned, indicating an interest in using this duality to study strongly coupled systems. In essence, this bibliography represents a research program exploring the deep connections between 2D quantum field theory, string theory, and black hole physics, with a focus on non-perturbative effects and the underlying microstates of black holes.

Gravity, Fluids, and Black Hole Entropy

This research investigates three-dimensional gravity with a negative cosmological constant, employing a novel approach to boundary conditions where chemical potentials are not fixed but dynamically determined. By utilizing a boundary Hamiltonian inspired by collective field theory, the study demonstrates a surprising connection between gravitational dynamics and one-dimensional fluid behaviour on a circle, with configurations mirroring known black hole geometries such as the BTZ black hole. The quantization of this system, achieved through bosonization of relativistic fermions, provides a microscopic description of black hole states, successfully matching the predicted Bekenstein-Hawking entropy. The results reveal that the partition function closely resembles that of chiral U(N) Yang-Mills theory, offering a new avenue for exploring corrections to the partition function itself. Importantly, the leading entropy term receives contributions from all possible configurations, while a specific logarithmic correction to the entropy is found to be one-loop exact and consistently equal to -1/2, regardless of whether the calculations are performed using the collective field theory or a relativistic fermion Hamiltonian. This consistency suggests a degree of universality in this one-loop correction.