Horatiu NastaseCambridge University Press, 9/21/2017EAN 9781107180383, ISBN10: 1107180384Hardcover, 628 pages, 25.3 x 19.3 x 3 cmLanguage: EnglishThe 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.PrefaceAcknowledgmentsIntroductionPart I. Condensed Matter Models and Problems1. Lightning review of statistical mechanics, thermodynamics, phases and phase transitions2. Magnetism in solids3. Electrons in solidsFermi gas vs. Fermi liquid4. Bosonic quasi-particlesphonons and plasmons5. Spin-charge separation in 1+1 dimensional solidsspinons and holons6. The Ising model and the Heisenberg spin chain7. Spin chains and integrable systems8. The thermodynamic Bethe ansatz9. Conformal field theories and quantum phase transitions10. Classical vs. quantum Hall effect11. SuperconductivityLandau-Ginzburg, London and BCS12. Topology and statisticsBerry and Chern-Simons, anyons and nonabelions13. Insulators14. The Kondo effect and the Kondo problem15. Hydrodynamics and transport propertiesfrom Boltzmann to Navier-StokesPart II. Elements of General Relativity and String Theory16. The Einstein equation and the Schwarzschild solution17. The Reissner-Nordstrom and Kerr-Newman solutions and thermodynamic properties of black holes18. Extra dimensions and Kaluza-Klein19. Electromagnetism and gravity in various dimensions. Consistent truncations20. Gravity plus matterblack holes and p-branes in various dimensions21. Weak/strong coupling dualities in 1+1, 2+1, 3+1 and d+1 dimensions22. The relativistic point particle and the relativistic string23. Lightcone strings and quantization24. D-branes and gauge fields25. Electromagnetic fields on D-branes. Supersymmetry and N = 4 SYM. T-duality of closed strings26. Dualities and M theory27. The AdS/CFT correspondencedefinition and motivationPart III. Applying String Theory to Condensed Matter Problems28. The pp wave correspondencestring Hamiltonian from N = 4 SYM29. Spin chains from N = 4 SYM30. The Bethe ansatzBethe strings from classical strings in AdS31. Integrability and AdS/CFT32. AdS/CFT phenomenologyLifshitz, Galilean and Schrodinger symmetries and their gravity duals33. Finite temperature and black holes34. Hot plasma equilibrium thermodynamicsentropy, charge density and chemical potential of strongly coupled theories35. Spectral functions and transport properties36. Dynamic and nonequilibrium properties of plasmaselectric transport, Langevin diffusion and thermalization via black hole quasi-normal modes37. The holographic superconductor38. The fluid-gravity correspondenceconformal relativistic fluids from black hole horizons39. Nonrelativistic fluidsfrom Einstein to Navier-Stokes and backPart IV. Advanced Applications40. Fermi gas and liquid in AdS/CFT41. Quantum Hall effect from string theory42. Quantum critical systems and AdS/CFT43. Particle-vortex duality and ABJM vs. AdS4 X CP3 duality44. Topology and non-standard statistics from AdS/CFT45. DBI scalar model for QGP/black hole hydro- and thermo-dynamics46. Holographic entanglement entropy in condensed matter47. Holographic insulators48. Holographic strange metals and the Kondo problemReferencesIndex.
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