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 NavierStokes 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. "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."--Résumé de l'éditeur "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." - publisher A comprehensive textbook covering 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 graduate students and researchers in both fields.