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.

29 pages, LaTeX, 3 figures; v2 references added

References in corpus (25)

• Black Hole Entropy is Noether Charge
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• The fuzzball proposal for black holes: an elementary review
• Bubbling AdS space and 1/2 BPS geometries
• EXTREMAL BLACK HOLES AND ELEMENTARY STRING STATES
• Statistical interpretation of Bekenstein entropy for systems with a stretched horizon
• Matrix Perturbation Theory For M-theory On a PP-Wave
• Fivebranes from gauge theory
• Transverse Fivebranes in Matrix Theory
• Superstars and Giant Gravitons
• Protected Multiplets of M-Theory on a Plane Wave
• Stretching the Horizon of a Higher Dimensional Small Black Hole
• On the Spectrum of PP-Wave Matrix Theory
• Embedding of theories with SU(2|4) symmetry into the plane wave matrix model
• Half-BPS Giants, Free Fermions and Microstates of Superstars
• N=4 SYM on R x S^3 and Theories with 16 Supercharges
• Rational foundation of GR in terms of statistical mechanic in the AdS/CFT framework
• Little String Theory from a Double-Scaled Matrix Model
• Coarse-graining 1/2 BPS geometries of type IIB supergravity
• Black Hole Statistics from Holography
• 1/2 BPS Geometries of M2 Giant Gravitons
• Stretched Horizon and Entropy of Superstars
• Little String Theory from Double-Scaling Limits of Field Theories
• General Lin-Maldacena solutions and PWMM Instantons from supergravity
• Half-BPS Geometries and Thermodynamics of Free Fermions

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• Statistical Physics of the Polarised IKKT Matrix Model
• Coarse-graining of bubbling geometries and the fuzzball conjecture