Quick introduction into AdS/CFT correspondence in physics of strongly correlated systems
https://doi.org/10.17586/2220-8054-2016-7-3-410-421
Abstract
The basic ideas of the AdS/CFT correspondence in physics of strongly correlated systems are briefly discussed. The application of the AdS/CFT correspondence for the Green’s functions derivation are shown.
Supporting agencies: This work was supported by the Russian Foundation for Basic Research under project No. 16-32-00230
About the Authors
M. B. Belonenko
Volgograd Institute of Business; Volgograd State University
Russian Federation
Russian Federation
Laboratory of Nanotechnology VIB.
400048, Volgograd; 400062, Volgograd
N. N. Konobeeva
Volgograd State University
Russian Federation
Russian Federation
400062, Volgograd
E. N. Galkina
Volgograd Institute of Business; Volgograd State Medical University
Russian Federation
Russian Federation
Laboratory of Nanotechnology
400048, Volgograd; 400131, Volgograd
References
1. Casalderrey-Solana J., Liu H., et al. Gauge/String Duality, Hot QCD and Heavy Ion Collisions. 2011, ArXiv:1101.0618.
2. Gubser S.S., Klebanov I.R., Polyakov A.M. Gauge theory correlators from noncritical string theory. Phys. Lett. B, 1998, 428, P. 105–114.
3. Hartnoll S.A. Lectures on holographic methods for condensed matter physics. Class. Quant. Grav., 2009, 26, 224002.
4. McGreevy J. Holographic duality with a view toward many-body physics. Adv. High Energy Phys., 2010, 723105.
5. D’Hoker E., Freedman D.Z. Supersymmetric gauge theories and the AdS/CFT correspondence. 2002, ArXiv: hep-th/0201253.
6. Witten E. Anti-de Sitter space and holography. Adv. Theor. Math. Phys., 1998, 2, P. 253–291.
7. Aharony O., Gubser S.S., et al. N field theories, string theory and gravity. Phys. Rept., 2000, 323, P. 183–386.
8. Maldacena J.M. The Large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys., 1998, 2, P. 231–252.
9. Zee A. Quantum Field Theory in a Nutshell, Princeton University Press, Princeton, 2010. 608 pp.
10. Balasubramanian V., Giddings S.B., Lawrence A. What do CFTs tell us about anti-de Sitter spacetimes. J. High Energy Phys., 1999, 03, 001.
11. Balasubramanian V., Kraus P., Lawrence A., Trivedi S.P. Holographic probes of anti-de Sitter spacetimes. Phys. Rev. D, 1999, 59, 104021.
12. Policastro G., Starinets A. On the absorption by near-extremal black branes. Nucl. Phys. B, 2001, 610, P. 117–143.
13. Danielsson U.H., Keski-Vakkuri E., Kruczenski M. Vacua, propagators, and holographic probes in AdS/CFT. J. High Energy Phys., 1999, 01, 002.
14. Balasubramanian V., Kraus P., Lawrence A. Bulk versus boundary dynamics in anti-de Sitter spacetime. Phys. Rev. D, 1999, 59, 046003.
15. Pak A.V., Belonenko M.B., Dyachkov P.N. Electrophysical properties of CNT. The augmented cylindrical wave method. Nanosystems: physics, chemistry, mathematics, 2013, 4(4), P. 564–569.
16. Herzog C.P. Lectures on holographic superfluidity and superconductivity. J. Phys. A, 2009, 42, 343001.
17. Cubrovic M., Zaanen J., Schalm K. String Theory, Quantum Phase Transitions and the Emergent Fermi-Liquid. Science, 2009, 325, P. 439–444.
18. Lee S.S. A non-Fermi liquid from a charged black hole: a critical Fermi ball. Phys.Rev. D, 2009, 79, 086006.
19. Senthil T., Vishwanath A., et al. Deconfined’ quantum critical points. Science, 2004, 303, P. 1490–1494.
20. Senthil T., Balents L., et al. Quantumcriticality beyond the Landau-Ginzburg-Wilson paradigm. Phys. Rev. B, 2004, 70, 144407.
21. Sachdev S. Quantun magnetism and criticality. Nature Phys., 2008, 4, P.! 173–185.
22. Jensen K., Kachru S., et al. Towards a holographic marginal Fermi liquid. Phys. Rev. D, 2011, 84, 126002.
23. Hartnoll S.A. Horizons, holography and condensed matter. 2011, ArXiv:1106.4324.
24. Liu H., McGreevy J., Vegh D. Non-fermi liquids from holography. Phys. Rev. D, 2011, 83, 065029.
25. Horowitz G.T. Introduction to holographic superconductors. 2010, ArXiv:1002.1722.
26. Iqbal N., Liu H. Real-time response in AdS/CFT with application to spinors. 2009, ArXiv: 0903.2596.
27. Iqbal N., Liu H. Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm. Phys. Rev. D, 2009, 79, 025023.
28. Benfatto G., Gallavotti G. Perturbation Theory of the Fermi Surface in a quantum liquid. A general quasiparticle formalism and onedimensional systems. Journal of Statistical Physics, 1990, 59, P. 541–664.
29. Shankar R. Statistical Mechanics and its Applications. Physica A, 1991, 177, P. 530–536.
30. Polchinski J. Effective field theory and the Fermi surface. 1992, Arxiv: hep-th/9210046.
31. Romans L.J. Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory. Nucl. Phys. B, 1992, 383, P. 395–415.
32. Bagger J., Lambert N. Gauge symmetry and supersymmetry of multiple M2-branes. JHEP, 2008, 02, P. 105.
33. Gustavsson A. Algebraic Structures on Parallel M2-Branes. Nucl. Phys. B, 2009, 811, P. 66.
34. Anderson P.W. Luttinger-liquid” behavior of the normal metallic state of the 2D Hubbard model. Phys. Rev. Lett., 1990, 64, 1839.
35. Chamblin A., Emparan R., Johnson C.V., Myers R.C. Charged AdS black holes and catastrophic holography. Phys. Rev. D, 1999, 60, 064018.
36. Varma C.M., Littlewood P.B., et al. Phenomenology of the normal state of Cu-O high-temperature superconductors. Phys. Rev. Lett., 1989, 63, 1996.
37. Varma C.M., Nussinov Z., van Saarloos W. Singular or non-Fermi liquids. Physics Reports, 2002, 361 (6), P. 267–417.
38. Shankar R. Renormalization-group approach to interacting fermions. Rev. Mod. Phys., 1994, 66, P. 129.
39. Gauntlett J.P. Varela. O. Consistent Kaluza-Klein reductions for general supersymmetric AdS solutions. Phys. Rev. D, 2007, 76, 126007.
40. Ramallo A.V. Introduction to the AdS/CFT correspondence. 2013, ArXiv:1310.4319.
41. Gubser S.S., Ren J. Analytic fermionic Green‘s functions from holography. Phys. Rev. D, 2012, 86, 046004.
42. Faulkner T., Liu H., J. McGreevy, Vegh D. Emergent quantum criticality, Fermi surfaces, and AdS2. Phys. Rev. D, 2011, 83, 125002.
43. Wang J. Schrodinger Fermi Liquids. Phys. Rev. D, 2014, 89 (4), 046008.
44. Belonenko M.B., Konobeeva N.N., Galkina E.N. Dynamics of few cycle optical pulses in a non-Fermi liquid and AdS/CFT correspondence. Mod. Phys. Lett. B, 2015, 29 (19), 15500965.
45. Dey P., Roy S. Zero sound in strange metals with hyperscaling violation from holography. Phys. Rev. D, 2013, 88, 046010.
46. Ryang S. The Hadamard function and the Feynman propagator in the AdS/CFT correspondence. Phys. Lett. B, 1999, 469, P. 87–95.
47. Jacobs V.P.J., Vandoren S.J.G., Stoof H.T.C. Holographic interaction effects on transport in Dirac semimetals. Phys. Rev. B, 2014, 90, 045108.
48. Wan X., Turner A.M., Vishwanath A., Savrasov S.Y. Opological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B, 2011, 83, 205101.
49. Burkov A.A., Balents L. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett., 2011, 107, 127205.
50. Faulkner T., Polchinski J. Semi-holographic Fermi liquid. JHEP, 2011, 06, P. 012.
51. Hoyos-Badajoz C., O’Bannon A., Wu J.M.S. Zero Sound in Strange Metallic Holography. JHEP, 2010, 1009, 086.
52. Levitov L.S., Shitov A.V. Green’s functions. Problems with solutions. Fizmatlit, Moscow, 2003, 392.
53. Basu P., Yang He J., Mukherjee A., Shieh H.H. Holographic Non-Fermi Liquid in a Background Magnetic Field. Phys. Rev. D, 2010, 82, 044036.
54. Gubankova E., Brill J., et al. Strongly Interacting Matter in Magnetic Fields. Springer, Berlin, 2013, 553.
55. Edalati M., Leigh R.G., Lo K.W., Phillips P.W. Dynamical Gap and Cuprate-like Physics from Holography. Phys. Rev. D, 2011, 83, 046012.
56. Vegh D. Fermi arcs from holography. 2010, Arxiv: 1007.0246.
57. Jain S. Universal thermal and electrical conductivity from holography. JHEP, 2010, 1011, P. 092.
58. Hashimoto K., Iizuka N. Impurities in Holography and Transport Coefficients. 2012, ArXiv:1207.4643.
59. Chesler P., Lucas A., Sachdev S. Conformal field theories in a periodic potential: Results from holography and field theory. Phys. Rev. D, 2014, 89, 026005.
60. Fan Z.-Y. Exact fermionic Green’s functions from holograpny. 2014, ArXiv:1407.0104.
61. Faulner T., Iqbal N., et al. Holographic non-Fermi-liquid fixed points. Philosophical transaction A, 2011, 369, P. 1941.
62. Liu H., McGreevy J., Vegh D. Non-Fermi liquids from holography. Phys. Rev. D, 2011, 83, 065029.
63. Sachdev S. A model of a Fermi-liquid using gauge-gravity duality. Phys. Rev. D, 2011, 84, 066009.
64. Herzog C.P., Kovtun P., Sachdev S., Son D.T. Quantum critical transport, duality, and M-theory. Phys. Rev. D, 2007, 75, 085020.
65. Sachdev S. Strange metals and the AdS/CFT correspondence. J. Stat. Mech., 2010, 1011, 11022.
66. Hartnoll S.A., Kovtun P.K., Mueller M., Sachdev S. Theory oft he Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes. Phys. Rev. B, 2007, 76, 144502.
67. Huijse L., Sachdev S. Fermi surfaces and gauge-gravity duality. Phys. Rev. D, 2011, 84, 026001.
68. Cremonini S. The shear viscosity to entropy ratio: A status report. Mod. Phys. Lett. B, 2011, 25 (23), P. 1867–1888.
69. Davison R.A., Goykhman M., Parnachev M. ADS/CFT and Landau-Fermi liquids. JHEP, 2014, 1407, P. 109.
70. Konobeeva N.N., Belonenko M.B. Propagation of few cycle optical pulses in marginal Fermi liquid and ADS/CFT correspondence. Physica B: Condensed Matter, 2015, 478, P. 43–46.
71. Zhukov A.V., Bouffanais R., Pak A.V., Belonenko M.B. Study of the indirect interaction in a non-Fermi liquid within the AdS/CFT correspondence framework. Mod. Phys. Lett. B, 2015, 29 (17), 1550081.
72. Konobeeva N.N., Belonenko M.B. Tunneling current in carbon nanotubes with deep impurities. Nanosystems: physics, chemistry, mathematics, 2013, 4 (4), P. 555–558.
Review
For citations:
Belonenko M.B., Konobeeva N.N., Galkina E.N. Quick introduction into AdS/CFT correspondence in physics of strongly correlated systems. Nanosystems: Physics, Chemistry, Mathematics. 2016;7(3):410-421. https://doi.org/10.17586/2220-8054-2016-7-3-410-421
Views:
4
Email this article 