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The library of Babel: On the Origin of Gravitational Thermodynamics
"... We show that heavy pure states of gravity can appear to be mixed states to almost all probes. For AdS5 Schwarzschild black holes, our arguments are made using the field theory dual to string theory in such spacetimes. Our results follow from applying information theoretic notions to field theory ope ..."
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Cited by 86 (17 self)
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We show that heavy pure states of gravity can appear to be mixed states to almost all probes. For AdS5 Schwarzschild black holes, our arguments are made using the field theory dual to string theory in such spacetimes. Our results follow from applying information theoretic notions to field theory operators capable of describing very heavy states in gravity. For half-BPS states of the theory which are incipient black holes, our account is exact: typical microstates are described in gravity by a spacetime “foam”, the precise details of which are almost invisible to almost all probes. We show that universal low-energy effective description of a foam of given global charges is via certain singular spacetime geometries. When one of the specified charges is the number of D-branes, the effective singular geometry is the half-BPS “superstar”. We propose this as the general mechanism by which the effective thermodynamic character of gravity emerges.
Half-bps geometries and thermodynamics of free fermions
- JHEP
"... Solutions of type IIB supergravity which preserve half of the supersymmetries have a dual description in terms of free fermions, as elucidated by the “bubbling AdS ” construction of Lin, Lunin and Maldacena. In this paper we study the half-BPS geometry associated with a gas of free fermions in therm ..."
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Cited by 10 (2 self)
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Solutions of type IIB supergravity which preserve half of the supersymmetries have a dual description in terms of free fermions, as elucidated by the “bubbling AdS ” construction of Lin, Lunin and Maldacena. In this paper we study the half-BPS geometry associated with a gas of free fermions in thermodynamic equilibrium obeying the Fermi-Dirac distribution. We consider both regimes of low and high temperature. In the former case, we present a detailed computation of the ADM mass of the supergravity solution and find agreement with the thermal energy of the fermions. The solution has a naked null singularity and, by general arguments, is expected to develop a finite area horizon once stringy corrections are included. By introducing a stretched horizon, we propose a way to match the entropy of the fermions with the entropy of the geometry in the low temperature regime. In the opposite limit of high temperature, the solution resembles a dilute gas of D3 branes. Also in this case the ADM mass of the geometry agrees with the thermal energy of the fermions.
From gravitons to giants
"... Abstract: We discuss exact quantization of gravitational fluctuations in the half-BPS sector around AdS5×S 5 background, using the dual super Yang-Mills theory. For this purpose we employ the recently developed techniques for exact bosonization of a finite number N of fermions in terms of N bosonic ..."
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Abstract: We discuss exact quantization of gravitational fluctuations in the half-BPS sector around AdS5×S 5 background, using the dual super Yang-Mills theory. For this purpose we employ the recently developed techniques for exact bosonization of a finite number N of fermions in terms of N bosonic oscillators. An exact computation of the three-point correlation function of gravitons for finite N shows that they become strongly coupled at sufficiently high energies, with an interaction that grows exponentially in N. We show that even at such high energies a description of the bulk physics in terms of weakly interacting particles can be constructed. The single particle states providing such a description are created by our bosonic oscillators or equivalently these are the multi-graviton states corresponding to the so-called Schur polynomials. Both represent single giant graviton states in the bulk. Multi-particle states corresponding to multi-giant gravitons are, however, different, since interactions among our bosons vanish identically, while the Schur polynomials are weakly interacting at high enough energies. Keywords: Bosonization, AdS-CFT, String Theory, Supergravity. Contents
Coarse-Graining the Lin-Maldacena Geometries
, 705
"... 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 ..."
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Cited by 5 (0 self)
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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 Recently, several fascinating new examples of gauge-theory / gravity duality have emerged [1] for which the field theory has a discrete highly degenerate basis of vacuum
What is the dual of a dipole?
, 2005
"... We study gravitational solutions that admit a dual CFT description and carry non zero dipole charge. We focus on the black ring solution in AdS3×S 3 and extract from it the onepoint functions of all CFT operators dual to scalar excitations of the six-dimensional metric. In the case of small black ri ..."
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Cited by 2 (1 self)
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We study gravitational solutions that admit a dual CFT description and carry non zero dipole charge. We focus on the black ring solution in AdS3×S 3 and extract from it the onepoint functions of all CFT operators dual to scalar excitations of the six-dimensional metric. In the case of small black rings, characterized by the level N, angular momentum J and dipole charge q3, we show how the large N and J dependence of the one-point functions can be reproduced, under certain assumptions, directly from a suitable ensemble in the dual CFT. Finally we present a simple toy model that describes the thermodynamics of the small black ring for arbitrary values of the dipole charge. Contents
Microstate Dependence of Scattering from the D1-D5 System
, 812
"... We investigate the question of distinguishing between different microstates of the D1-D5 system with charges Q1 and Q5, by scattering with a supergravity mode which is a minimally coupled scalar in the leading supergravity approximation. The scattering is studied in the dual CFT description in the o ..."
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We investigate the question of distinguishing between different microstates of the D1-D5 system with charges Q1 and Q5, by scattering with a supergravity mode which is a minimally coupled scalar in the leading supergravity approximation. The scattering is studied in the dual CFT description in the orbifold limit for finite R, where R is the radius of the circle on which the D1 branes are wrapped. Even though the system has discrete energy levels for finite R, an absorption probability proportional to time is found when the ingoing beam has a finite width ∆E which is much larger than the inverse of the time scale T. When R∆E ≫ 1, the absorption crosssection is found to be independent of the microstate and identical to the leading semiclassical answer computed from the naive geometry. For smaller ∆E, the answer depends on the particular microstate, which we examine for typical as well as for atypical microstates and derive an upper bound for the leading correction for either a Lorentzian or a Gaussian energy profile of the incoming beam. When 1/R ≫ ∆E ≫ the average energy gap ( 1/(R √ Q1Q5) ), we find that in a typical state the bound is proportional to the area of the stretched horizon, Q1Q5, up to log(Q1Q5) terms. Furthermore, when the central energy in the incoming beam,
The Gravitational Description of Coarse Grained
, 2006
"... In this paper we construct a detailed map from pure and mixed half-BPS states of the D1-D5 system to half-BPS solutions of type IIB supergravity. Using this map, we can see how gravity arises through coarse graining microstates, and we can explicitly confirm the microscopic description of conical de ..."
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In this paper we construct a detailed map from pure and mixed half-BPS states of the D1-D5 system to half-BPS solutions of type IIB supergravity. Using this map, we can see how gravity arises through coarse graining microstates, and we can explicitly confirm the microscopic description of conical defect metrics, the M = 0 BTZ black hole and of small black rings. We find that the entropy associated to the natural geometric stretched horizon typically exceeds that of the mixed state from which the geometry was obtained. Contents
YITP-SB-05-44 hep-th/0512101 Half-BPS Geometries and
, 2005
"... Solutions of type IIB supergravity which preserve half of the supersymmetries have a dual description in terms of free fermions, as elucidated by the “bubbling AdS ” construction of Lin, Lunin and Maldacena. In this paper we study the half-BPS geometry associated with a gas of free fermions in therm ..."
Abstract
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Solutions of type IIB supergravity which preserve half of the supersymmetries have a dual description in terms of free fermions, as elucidated by the “bubbling AdS ” construction of Lin, Lunin and Maldacena. In this paper we study the half-BPS geometry associated with a gas of free fermions in thermodynamic equilibrium obeying the Fermi-Dirac distribution. We consider both regimes of low and high temperature. In the former case, we present a detailed computation of the ADM mass of the supergravity solution and find agreement with the thermal energy of the fermions. The solution has a naked null singularity and, by general arguments, is expected to develop a finite area horizon once stringy corrections are included. By introducing a stretched horizon, we propose a way to match the entropy of the fermions with the entropy of the geometry in the low temperature regime. In the opposite limit of high temperature, the solution resembles a dilute gas of D3 branes. Also in this case the ADM mass of the geometry agrees with the thermal energy of the fermions.
