Summaries

toc =Discussion session=

What can AdS/CFT do? What has been achieved?
 * describes nontrivial fixed points (are they stable? can they be classified?)
 * allows computations in these fixed points.
 * allows deformations away from critical points.
 * geometrises the RG flow.
 * easily generalised to finite T/mu/B/condensates.
 * real time linear response very easy.
 * non equilibrium and nonlinear response.
 * fermi-surface like signatures in fermionic response at finite mu.
 * superfluid phase transitions.
 * probe boundaries of hydrodynamic descriptions.
 * in principle can add a lattice but need to solve PDEs.

What known cond.mat problems might be relevant?
 * pairing in cuprates.
 * gapless spin liquids.
 * deconfined "quarks" at finite charge density.
 * cold atoms out of equilibrium.
 * novel quantum Hall phases (magnetic phases in 3d).
 * SLEs?
 * critical exponents.

What are the main limitations of AdS/CFT?
 * "AdS/CFT" should be renamed "string/field" or "gauge/gravity" or "holography".
 * Restricted to theories with matrix valued fields? large N^2?
 * Need supersymmetry? (probably not in principle)
 * intermediate values of the coupling?

What new problems/approaches might AdS/CFT suggest?
 * thinking without quasiparticles at any intermediate step.
 * RHIC analogues in condensed matter
 * what can happen at finite density -- exotic phases of matter.
 * what is entropy?

=Special challenges of QCP= (from Sondhi's lecture)
 * T>0 requires scaling __functions__ (rather than just numbers).
 * Real time response is tough.
 * Complex actions (Berry phases).
 * Soft modes.
 * Non-order parameter transitions. eg. critical fermions, deconfined criticality, localisation, infinite disorder fixed points.