Coarse-graining 1/2 BPS geometries of type IIB supergravity

TL;DR

The paper investigates whether finite-temperature coarse-graining of the 1/2 BPS LLM geometries can generate a Schwarzschild-like horizon in type IIB supergravity on $AdS_5\times S^5$ by mapping the finite-$T$ Fermi distribution to the LLM source $z^T(r,y)$. The approach leverages the dual free-fermion phase-space picture to construct the corresponding supergravity background and derives a low-$T$ expansion, with $\gamma = \frac{2 \pi^2 T^2 \hbar^2}{3 r_0^4} = \frac{\pi^2 T^2}{6 N^2}$, yielding analytic expressions for the metric components in the nearly degenerate limit. The main result shows a horizonless, singularity-free geometry at finite $T$, indicating that horizon formation likely requires coarse-graining over the full Hilbert space of IIB string excitations rather than only the half-BPS sector. This work clarifies the role of sector restriction in holographic coarse-graining and motivates future investigations into full-string coarse-graining, ADM mass matching, and entropy encoding within these backgrounds.

Abstract

Recently Lin, Lunin and Maldacena (LLM) (hep-th/0409174) explicitly mapped 1/2 BPS excitations of type IIB supergravity on AdS_5 x S^5 into free fermion configurations. We discuss thermal coarse-gaining of LLM geometries by explicitly mapping the corresponding equilibrium finite temperature fermion configuration into supergravity. Following Mathur conjecture, a prescription of this sort should generate a horizon in the geometry. We did not find a horizon in finite temperature equilibrium LLM geometry. This most likely is due to the fact that coarse-graining is performed only in a half-BPS sector of the full Hilbert space of type IIB supergravity. For temperatures much less than the AdS curvature scale the equilibrium background corresponding to nearly degenerate dual fermi-gas is found analytically.