标题： 玻色化，BTZ 黑洞微观态，以及熵的对数修正 显示英文标题

标题： Bosonization, BTZ Black Hole Microstates, and Logarithmic Correction to Entropy

摘要： 我们研究在非标准边界条件下具有负宇宙常数的三维引力，其中化学势由动力学确定。 使用受集体场理论（ColFT）启发的边界哈密顿量，边界动力学简化为圆周上一维流体的动力学，其配置对应于如BTZ黑洞等的体几何结构。 通过相对论费米子的玻色化对系统进行量子化，我们得到了以杨图形式描述黑洞态的微观描述，其简并度与贝肯斯坦-霍金熵相符。 我们计算了ColFT哈密顿量和相对论自由费米子哈密顿量的欧几里得规范配分函数和自由能。 在ColFT情况下，配分函数类似于环面上的chiral U(N)杨-米尔斯理论，其中N~1/(\beta G)。 这提供了一种计算配分函数量子修正的新方法。 主导的熵项来自所有亏格，而次主导的对数修正是一圈精确的，仅来自亏格一部分，系数为-1/2。 该系数在相对论费米子情况下保持不变，表明一圈修正在不同边界哈密顿量之间具有普遍性。 显示英文摘要

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/(\beta G). 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 -1/2 . This coefficient remains unchanged in the relativistic fermion case, suggesting the universality of the one-loop correction across different boundary Hamiltonians.