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Register a new userDiffusion in an Expanding Plasma using AdS/CFT
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We consider the diffusion of a non-relativistic heavy quark of fixed mass M, in a one-dimensionally expanding and strongly coupled plasma using the AdS/CFT duality. The Greens function constructed around a static string embedded in a background with a moving horizon, is identified with the noise correlation function in a Langevin approach. The (electric) noise decorrelation is of order 1/T(tau) while the velocity de-correlation is of order MD(tau)/T(tau). For MD>1, the diffusion regime is segregated and the energy loss is Langevin-like. The time dependent diffusion constant D(tau) asymptotes its adiabatic limit 2/pisqrt{lambda} T(tau) when tau/tau_0=(1/3eta_0tau_0)^3 where eta_0 is the drag coefficient at the initial proper time tau_0.
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We discuss an exact time dependent O(3) symmetric solution with a horizon of the 5d AdS classical gravity equations searching for a 4d boundary theory which would correspond to expanding gauge theory matter. The boundary energy-momentum tensor and entropy density are computed. The boundary metric is the flat Friedmann one and any time dependence on the boundary is incompatible with Minkowski metric. However, at large times when curvature effects are negligible, perfect fluid behavior arises in a natural way.
We consider the effect of an expanding plasma on probe matter by determining time-dependent D7 embeddings in the holographic dual of an expanding viscous plasma. We calculate the chiral condensate and meson spectra including contributions of viscosity. The chiral condensate essentially confirms the expectation from the static black hole. For the meson spectra we propose a scheme that is in agreement with the adiabatic approximation. New contributions arise for the vector mesons at the order of the viscosity terms.
The eikonalized parton-parton scattering amplitude at large $sqrt{s}$ and large impact parameter, is dominated by the exchange of a hyperbolic surface in walled AdS. Its analytical continuation yields a worldsheet instanton that is at the origin of the Reggeization of the amplitude and a thermal-like quantum entropy ${cal S}_T$. We explicitly construct the entangled density matrix following from the exchanged surface, and show that its von-Neumann entanglement entropy ${cal S}_E$ coincides with the thermal-like entropy, i.e. ${cal S}_T={cal S}_E$. The ratio of the entanglement entropy to the transverse growth of the exchanged surface is similar to the Bekenstein entropy ratio for a black-hole, with a natural definition of saturation and the on-set of chaos in high energy collisions. The largest eigenvalues of the entangled density matrix obey a cascade equation in rapidity, reminiscent of non-linear QCD evolution of wee-dipoles at low-x and weak coupling. We suggest that the largest eigenvalues describe the probability distributions of wee-quanta at low-x and strong coupling that maybe measurable at present and future pp and ep colliders.
In this paper we study in detail the deformations introduced in [1] of the integrable structures of the AdS$_{2,3}$ integrable models. We do this by embedding the corresponding scattering matrices into the most general solutions of the Yang-Baxter equation. We show that there are several non-trivial embeddings and corresponding deformations. We work out crossing symmetry for these models and study their symmetry algebras and representations. In particular, we identify a new elliptic deformation of the $rm AdS_3 times S^3 times M^4$ string sigma model.
We define a holographic dual to the Donaldson-Witten topological twist of $mathcal{N}=2$ gauge theories on a Riemannian four-manifold. This is described by a class of asymptotically locally hyperbolic solutions to $mathcal{N}=4$ gauged supergravity in five dimensions, with the four-manifold as conformal boundary. Under AdS/CFT, minus the logarithm of the partition function of the gauge theory is identified with the holographically renormalized supergravity action. We show that the latter is independent of the metric on the boundary four-manifold, as required for a topological theory. Supersymmetric solutions in the bulk satisfy first order differential equations for a twisted $Sp(1)$ structure, which extends the quaternionic Kahler structure that exists on any Riemannian four-manifold boundary. We comment on applications and extensions, including generalizations to other topological twists.
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