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<p>We study three-dimensional gravity with negative cosmological constant under non-standard boundary conditions where chemical potentials are determined dynamically. Using a boundary Hamiltonian inspired by collective field theory (ColFT), the boundary dynamics reduce to those of a one-dimensional fluid on a circle, with configurations corresponding to bulk geometries such as BTZ black holes. Quantizing the system via bosonization of relativistic fermions, we obtain a microscopic description of black hole states in terms of Young diagrams, whose degeneracies match the Bekenstein-Hawking entropy.</p><p>We compute the Euclidean canonical partition function and free energy for both the ColFT Hamiltonian and a relativistic free-fermion Hamiltonian. In the ColFT case, the partition function resembles that of chiral U(<i>N</i>) Yang-Mills theory on a torus, with <i>N</i> ~ 1/(<i>βG</i>). This offers a novel way to compute quantum corrections to the partition function. The leading entropy term receives contributions from all genera, while the subleading logarithmic correction is one-loop exact, arising solely from the genus-one sector with coefficient <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(-\frac{1}{2}\)</EquationSource> </InlineEquation>. This coefficient remains unchanged in the relativistic fermion case, suggesting the universality of the one-loop correction across different boundary Hamiltonians.</p>

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Bosonization, BTZ black hole microstates, and logarithmic correction to entropy

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月8日

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  • Suvankar Dutta,
  • Shruti Menon,
  • Aayush Srivastav

摘要

We study three-dimensional gravity with negative cosmological constant under non-standard boundary conditions where chemical potentials are determined dynamically. Using a boundary Hamiltonian inspired by collective field theory (ColFT), the boundary dynamics reduce to those of a one-dimensional fluid on a circle, with configurations corresponding to bulk geometries such as BTZ black holes. Quantizing the system via bosonization of relativistic fermions, we obtain a microscopic description of black hole states in terms of Young diagrams, whose degeneracies match the Bekenstein-Hawking entropy.

We compute the Euclidean canonical partition function and free energy for both the ColFT Hamiltonian and a relativistic free-fermion Hamiltonian. In the ColFT case, the partition function resembles that of chiral U(N) Yang-Mills theory on a torus, with N ~ 1/(βG). This offers a novel way to compute quantum corrections to the partition function. The leading entropy term receives contributions from all genera, while the subleading logarithmic correction is one-loop exact, arising solely from the genus-one sector with coefficient \(-\frac{1}{2}\) . This coefficient remains unchanged in the relativistic fermion case, suggesting the universality of the one-loop correction across different boundary Hamiltonians.