String Theory Methods for Condensed Matter Physics

The discovery of a duality between Anti-de Sitter spaces (AdS) and Conformal Field Theories (CFT) has led to major advances in our understanding of quantum field theory and quantum gravity. String theory methods and AdS/CFT correspondence maps provide new ways to think about difficult condensed matter problems. String theory methods based on the AdS/CFT correspondence allow us to transform problems so they have weak interactions and can be solved more easily. They can also help map problems to different descriptions, for instance mapping the description of a fluid using the Navier–Stokes equations to the description of an event horizon of a black hole using Einstein's equations. This textbook covers the applications of string theory methods and the mathematics of AdS/CFT to areas of condensed matter physics. Bridging the gap between string theory and condensed matter, this is a valuable textbook for students and researchers in both fields.

Preface; Acknowledgments; Introduction; Part I. Condensed Matter Models and Problems: 1. Lightning review of statistical mechanics, thermodynamics, phases and phase transitions; 2. Magnetism in solids; 3. Electrons in solids: Fermi gas vs. Fermi liquid; 4. Bosonic quasi-particles: phonons and plasmons; 5. Spin-charge separation in 1+1 dimensional solids: spinons and holons; 6. The Ising model and the Heisenberg spin chain; 7. Spin chains and integrable systems; 8. The thermodynamic Bethe ansatz; 9. Conformal field theories and quantum phase transitions; 10. Classical vs. quantum Hall effect; 11. Superconductivity: Landau-Ginzburg, London and BCS; 12. Topology and statistics: Berry and Chern-Simons, anyons and nonabelions; 13. Insulators; 14. The Kondo effect and the Kondo problem; 15. Hydrodynamics and transport properties: from Boltzmann to Navier-Stokes; Part II. Elements of General Relativity and String Theory: 16. The Einstein equation and the Schwarzschild solution; 17. The Reissner-Nordstrom and Kerr-Newman solutions and thermodynamic properties of black holes; 18. Extra dimensions and Kaluza-Klein; 19. Electromagnetism and gravity in various dimensions. Consistent truncations; 20. Gravity plus matter: black holes and p-branes in various dimensions; 21. Weak/strong coupling dualities in 1+1, 2+1, 3+1 and d+1 dimensions; 22. The relativistic point particle and the relativistic string; 23. Lightcone strings and quantization; 24. D-branes and gauge fields; 25. Electromagnetic fields on D-branes. Supersymmetry and N = 4 SYM. T-duality of closed strings; 26. Dualities and M theory; 27. The AdS/CFT correspondence: definition and motivation; Part III. Applying String Theory to Condensed Matter Problems: 28. The pp wave correspondence: string Hamiltonian from N = 4 SYM; 29. Spin chains from N = 4 SYM; 30. The Bethe ansatz: Bethe strings from classical strings in AdS; 31. Integrability and AdS/CFT; 32. AdS/CFT phenomenology: Lifshitz, Galilean and Schr odinger symmetries and their gravity duals; 33. Finite temperature and black holes; 34. Hot plasma equilibrium thermodynamics: entropy, charge density and chemical potential of strongly coupled theories; 35. Spectral functions and transport properties; 36. Dynamic and nonequilibrium properties of plasmas: electric transport, Langevin diffusion and thermalization via black hole quasi-normal modes; 37. The holographic superconductor; 38. The fluid-gravity correspondence: conformal relativistic fluids from black hole horizons; 39. Nonrelativistic fluids: from Einstein to Navier-Stokes and back; Part IV. Advanced Applications: 40. Fermi gas and liquid in AdS/CFT; 41. Quantum Hall effect from string theory; 42. Quantum critical systems and AdS/CFT; 43. Particle-vortex duality and ABJM vs. AdS4 X CP3 duality; 44. Topology and non-standard statistics from AdS/CFT; 45. DBI scalar model for QGP/black hole hydro- and thermo-dynamics; 46. Holographic entanglement entropy in condensed matter; 47. Holographic insulators; 48. Holographic strange metals and the Kondo problem; References; Index.

Horatiu Nastase is a Researcher at the Institute for Theoretical Physics at the Universidade Estadual Paulista, São Paulo. To date, his career has spanned four continents. As an undergraduate he studied at Universitatea din Bucure?ti, Romania and University of Copenhagen. He later completed his Ph.D. at the State University of New York, Stony Brook, before moving to the Institute for Advanced Study, Princeton, where his collaboration with David Berenstein and Juan Maldacena defined the pp-wave correspondence. He has also held research and teaching positions at Brown University and the Tokyo Institute of Technology.