AdS/CFT connection between Boltzmann and Einstein equations: Kinetic theory and pure gravity in AdS space

Journal Article · Thu Apr 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.086005· OSTI ID:21409673

Iyer, Ramakrishnan ^[1]; Mukhopadhyay, Ayan ^[2]

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1. Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089-0484 (United States)
2. Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211019 (India)

The AdS/CFT correspondence defines a sector with universal strongly coupled dynamics in the field theory as the dual of pure gravity in AdS described by Einstein's equation with a negative cosmological constant. We explain here, from the field-theoretic viewpoint how the dynamics in this sector gets determined by the expectation value of the energy-momentum tensor alone. We first show that the Boltzmann equation has very special solutions which could be functionally completely determined in terms of the energy-momentum tensor alone. We call these solutions conservative solutions. We indicate why conservative solutions should also exist when we refine this kinetic description to go closer to the exact microscopic theory or even move away from the regime of weak coupling so that no kinetic description could be employed. We argue that these conservative solutions form the universal sector dual to pure gravity at strong coupling and large N. Based on this observation, we propose a regularity condition on the energy-momentum tensor so that the dual solution in pure gravity has a smooth future horizon. We also study if irreversibility emerges only at long time scales of observation, unlike the case of the Boltzmann equation.

• OSTI ID: 21409673
• Journal Information: Physical Review. D, Particles Fields, Vol. 81, Issue 8; Other Information: DOI: 10.1103/PhysRevD.81.086005; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANTI DE SITTER SPACE
BOLTZMANN EQUATION
COSMOLOGICAL CONSTANT
EINSTEIN FIELD EQUATIONS
ENERGY-MOMENTUM TENSOR
EXPECTATION VALUE
FIELD THEORIES
GRAVITATION
MATHEMATICAL SOLUTIONS
QUANTUM FIELD THEORY
SPACE
STRONG-COUPLING MODEL
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD EQUATIONS
INTEGRO-DIFFERENTIAL EQUATIONS
KINETIC EQUATIONS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
TENSORS