ABSTRACT

Sean Hartnoll Harvard University, Department of Physics, Jefferson Laboratory, Cambridge, MA 02138, U.S.A.

Free or weakly-interacting field theories underpin a great deal of our physical intuition. The fact that effective weakly-interacting quasi-particles can emerge even when the fundamental microscopic degrees of freedom are strongly interacting, as illustrated dramatically by Landau’s theory of Fermi liquids [1], has allowed great progress in physics without confronting head-on the problem of strong coupling. Even where genuinely strongly-interacting physics is required, for instance at the Wilson-Fisher fixed point in 2+1 dimensions, computational techniques such as the (vector) large-N or 4− expansions allow us to move the problem into a weakly-coupled regime. At small or large N one can compute, using weak-coupling notions such as single-particle propagators, and then extrapolate back to the physical values of = 1 or N = 2, 3. Remarkably, this procedure often gives qualitative and even quantitatively correct answers. However, such expansions are difficult and less accurate for real time correlators at finite temperature, as described in Chap. 1 and [2].