Parton picture for the strongly coupled SYM plasma

Deep inelastic scattering off the strongly coupled N=4 supersymmetric Yang-Mills plasma at finite temperature can be computed within the AdS/CFT correspondence, with results which are suggestive of a parton picture for the plasma. Via successive branchings, essentially all partons cascade down to very small values of the longitudinal momentum fraction x and to transverse momenta smaller than the saturation momentum Q_s\sim T/x. This scale Q_s controls the plasma interactions with a hard probe, in particular, the jet energy loss and its transverse momentum broadening.Comment: 4 pages, Talk given at Quark Matter 2008: 20th International Conference on Ultra-Relativistic Nucleus Nucleus Collisions (QM 2008), Jaipur, India, 4-10 Feb 200

ABJM theory as a Fermi gas

The partition function on the three-sphere of many supersymmetric Chern-Simons-matter theories reduces, by localization, to a matrix model. We develop a new method to study these models in the M-theory limit, but at all orders in the 1/N expansion. The method is based on reformulating the matrix model as the partition function of an ideal Fermi gas with a non-trivial, one-particle quantum Hamiltonian. This new approach leads to a completely elementary derivation of the N^{3/2} behavior for ABJM theory and N=3 quiver Chern-Simons-matter theories. In addition, the full series of 1/N corrections to the original matrix integral can be simply determined by a next-to-leading calculation in the WKB or semiclassical expansion of the quantum gas, and we show that, for several quiver Chern-Simons-matter theories, it is given by an Airy function. This generalizes a recent result of Fuji, Hirano and Moriyama for ABJM theory. It turns out that the semiclassical expansion of the Fermi gas corresponds to a strong coupling expansion in type IIA theory, and it is dual to the genus expansion. This allows us to calculate explicitly non-perturbative effects due to D2-brane instantons in the AdS background.Comment: 52 pages, 11 figures. v3: references, corrections and clarifications added, plus a footnote on the relation to the recent work by Hanada et a