Derive BTZ entropy from the matrix model partition function

Derive the Bekenstein–Hawking entropy of the BTZ black hole directly from the U(N) composite-field matrix model by computing the matrix-model partition function and showing that the resulting microstate count reproduces SBTZ = 2π r+/4G3 for the emergent BTZ geometry.

Background

In the paper, the BTZ black hole emerges from thermal backreaction of off‑diagonal composite modes, and its entropy is matched via the Cardy formula and scaling arguments. The authors also interpret microstates in terms of off‑diagonal composites and vortex degrees of freedom.

While these arguments provide strong evidence for SBTZ ~ N^2, the authors note that a detailed, first‑principles derivation from the matrix model partition function has not yet been carried out, leaving a concrete computational gap.