Coarse-Graining the Lin-Maldacena Geometries
Abstract
The Lin-Maldacena geometries are nonsingular gravity duals to degenerate vacuum states of a family of field theories with SU(2|4) supersymmetry. In this note, we show that at large N, where the number of vacuum states is large, there is a natural `macroscopic' description of typical states, giving rise to a set of coarse-grained geometries. For a given coarse-grained state, we can associate an entropy related to the number of underlying microstates. We find a simple formula for this entropy in terms of the data that specify the geometry. We see that this entropy function is zero for the original microstate geometries and maximized for a certain ``typical state'' geometry, which we argue is the gravity dual to the zero-temperature limit of the thermal state of the corresponding field theory. Finally, we note that the coarse-grained geometries are singular if and only if the entropy function is non-zero.
Keywords
Cite
@article{arxiv.0705.4308,
title = {Coarse-Graining the Lin-Maldacena Geometries},
author = {Hsien-Hang Shieh and Greg van Anders and Mark Van Raamsdonk},
journal= {arXiv preprint arXiv:0705.4308},
year = {2009}
}