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

A bstract 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.