String Theory Methods for Condensed Matter Physics
Cambridge University Press, 9/21/2017
EAN 9781107180383, ISBN10: 1107180384
Hardcover, 628 pages, 25.3 x 19.3 x 3 cm
Language: English
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 Schrodinger 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.