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

TL;DR

This paper investigates the effects of thermal coarse-graining on 1/2 BPS geometries in type IIB supergravity, finding no horizon formation at finite temperature within the studied sector, and analytically describing near-degenerate fermion configurations.

Contribution

It provides an explicit mapping of finite temperature fermion configurations to supergravity geometries and analyzes the absence of horizons in this context, extending the understanding of coarse-graining effects.

Findings

No horizon forms in finite temperature equilibrium LLM geometries.

Analytic solutions for nearly degenerate fermion configurations at low temperatures.

Coarse-graining in a half-BPS sector may be insufficient for horizon formation.

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.