String Theory and Holographic Duality

Part 1. Hints for holography

• Gravity v.s. all other interactions

  Weinberg–Witten no–go theorem

• Black holes and black hole thermodynamics
• Holographic principle

  Bekenstein bound

• QCD in the large Nc limit

Part 2. Introducing the gauge / gravity duality

• Motivating the duality
• A bit string theory
• The AdS / CFT conjecture

Part 3. A duality tool box

• General aspects of the duality
• Generalizations
• Correlation functions of local operators
• Wilson loops
• Entanglement entropy

Part 4. Holographic renormalization group flows

• Holographic renormalizations
• Hamilton-Jacobi approach
• Holographic Wilsonian renormalization group approach
• Some examples

Part 5. Insights into many-body systems

• Transports
• Hydrodynamics
• Quark-gluon plasmas
• Condensed matter applications:
  • non-Fermi liquids
  • holographic superfluids / superconductors
• Non-equilibrium physics

Part 6. Insights into quantum gravity

• Outstanding questions:
  • Spacelike singularities
  • Black hole information paradox
• Some clues

Part 7. Status of the duality