Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-05-30
JHEP 0709:059,2007
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, LaTeX, 3 figures; v2 references added
Scientific paper
10.1088/1126-6708/2007/09/059
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.
Anders Greg van
Raamsdonk Mark Van
Shieh Hsien-Hang
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