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Register a new userGravity dual of 1+1 dimensional Bjorken expansion
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We study the application of AdS/CFT duality to longitudinal boost invariant Bjorken expansion of QCD matter produced in ultrarelativistic heavy ion collisions. As the exact (1+4)-dimensional bulk solutions for the (1+3)-dimensional boundary theory are not known, we investigate in detail the (1+1)-dimensional boundary theory, where the bulk is AdS_3 gravity. We find an exact bulk solution, show that this solution describes part of the spinless Banados-Teitelboim-Zanelli (BTZ) black hole with the angular dimension unwrapped, and use the thermodynamics of the BTZ hole to recover the time-dependent temperature and entropy density on the boundary. After separating from the holographic energy-momentum tensor a vacuum contribution, given by the extremal black hole limit in the bulk, we find that the boundary fluid is an ideal gas in local thermal equilibrium. Including angular momentum in the bulk gives a boundary flow that is boost invariant but has a nonzero longitudinal velocity with respect to the Bjorken expansion.
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We find the three-dimensional gravity dual of a process in which two clouds of (1+1)-dimensional conformal matter moving in opposite directions collide. This gives the most general conformally invariant holographic flow in the 1+1 dimensional boundary theory in terms of two arbitrary functions. With a suitable choice of the arbitrary functions the process can be interpreted as an opaque collision of two extended systems with central, fragmentation and interaction regions. Comparison with classical gluon field calculations relates the size of the system with the saturation scale.
A class of explicitly integrable models of 1+1 dimensional dilaton gravity coupled to scalar fields is described in some detail. The equations of motion of these models reduce to systems of the Liouville equations endowed with energy and momentum constraints. The general solution of the equations and constraints in terms of chiral moduli fields is explicitly constructed and some extensions of the basic integrable model are briefly discussed. These models may be related to high dimensional supergravity theories but here they are mostly considered independently of such interpretations. A brief review of other integrable models of two-dimensional dilaton gravity is also given.
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