Multipoint correlators of conformal field theories: Implications for quantum critical transport

Physical Review B - Condensed Matter and Materials Physics

Volumn 87, Issue 8, 2013, Pages

  Chowdhury, Debanjan ^a   Raju, Suvrat ^b,c,d   Sachdev, Subir ^a   Singh, Ajay ^e,f   Strack, Philipp ^a  

^a HARVARD UNIVERSITY   (United States)

^b IISc Campus   (India)

^c HARISH CHANDRA RESEARCH INSTITUTE   (India)

^d INSTITUTE FOR ADVANCED STUDY   (United States)

^e UNIVERSITY OF WATERLOO   (Canada)

^f PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84874546691     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.87.085138     Document Type: Article

References (58)

1. J. M. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998);
2. S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B PYLBAJ 0370-2693 10.1016/S0370-2693(98)00377-3 428, 105 (1998).
3. E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998).
4. C. P. Herzog, P. Kovtun, S. Sachdev, and D. T. Son, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.75.085020 75, 085020 (2007).
5. R. C. Myers, S. Sachdev, and A. Singh, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.83.066017 83, 066017 (2011).
6. A. Ritz and J. Ward, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.79. 066003 79, 066003 (2009).
7. D. M. Hofman and J. Maldacena, J. High Energy Phys. JHEPAB 1126-6708 10.1088/1126-6708/2008/05/012 05 (2008) 012.
8. W. Witczak-Krempa and S. Sachdev, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.235115 86, 235115 (2012).
9. S. Sachdev, Annu. Rev. Condens. Matter Phys. ARCMCX 1947-5454 10.1146/annurev-conmatphys-020911-125141 3, 9 (2012).
10. X. Wen and Y. Wu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 70.1501 70, 1501 (1993);
11. W. Chen, M. Fisher, and Y. Wu, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.48.13749 48, 13749 (1993);
12. W. Rantner and X. G. Wen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.3871 86, 3871 (2001); (Pubitemid 32425353)
13. S. Sachdev, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.57.7157 57, 7157 (1998);
14. W. Rantner and X. G. Wen, Phys. Rev. B 1098-0121 10.1103/PhysRevB.66. 144501 66, 144501 (2002);
15. O. Motrunich and A. Vishwanath, Phys. Rev. B 1098-0121 10.1103/PhysRevB.70.075104 70, 075104 (2004);
16. T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M. P. A. Fisher, Science SCIEAS 0036-8075 10.1126/science.1091806 303, 1490 (2004); (Pubitemid 38314412)
17. T. Senthil, L. Balents, S. Sachdev, A. Vishwanath, and M. P. A. Fisher, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.70.144407 70, 144407 (2004); (Pubitemid 40052583)
18. M. Hermele, T. Senthil, M. P. A. Fisher, P. A. Lee, N. Nagaosa, and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.70.214437 70, 214437 (2004); (Pubitemid 40239483)
19. M. Hermele, T. Senthil, and M. P. A. Fisher, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.72.104404 72, 104404 (2005); (Pubitemid 43022367)
20. R. Kaul, Y. Kim, S. Sachdev, and T. Senthil, Nat. Phys. NPAHAX 1745-2473 10.1038/nphys790 4, 28 (2007).
21. R. Kaul and S. Sachdev, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.155105 77, 155105 (2008).
22. I. R. Klebanov, S. S. Pufu, S. Sachdev, and B. R. Safdi, J. High Energy Phys. JHEPFG 1126-6708 10.1007/JHEP05(2012)036 05 (2012) 036.
23. H. Osborn and A. Petkou, Ann. Phys. APNYA6 0003-4916 10.1006/aphy.1994. 1045 231, 311 (1994).
24. J. L. Cardy, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(87)90192-1 290, 355 (1987).
25. A. Buchel, J. Escobedo, R. C. Myers, M. F. Paulos, A. Sinha, and M. Smolkin, J. High Energy Phys. JHEPFG 1126-6708 10.1007/JHEP03(2010)111 03 (2010) 111.
26. R. C. Myers, M. F. Paulos, and A. Sinha, J. High Energy Phys. JHEPFG 1126-6708 10.1007/JHEP08(2010)035 08 (2010) 035.
27. S. Giombi and X. Yin, arXiv: 1208.4036;
28. S. Giombi, S. Minwalla, S. Prakash, S. P. Trivedi, S. R. Wadia, and X. Yin, Eur. Phys. J. C EPCFFB 1434-6044 10.1140/epjc/s10052-012-2112-0 72, 2112 (2012);
29. J. Maldacena and A. Zhiboedov, arXiv: 1112.1016;
30. O. Aharony, G. Gur-Ari, and R. Yacoby, J. High Energy Phys. JHEPFG 1126-6708 10.1007/JHEP12(2012)028 12 (2012) 028.
31. L. J. Dixon, arXiv: hep-ph/9601359.
32. J. M. Maldacena and G. L. Pimentel, J. High Energy Phys. JHEPFG 1126-6708 10.1007/JHEP09(2011)045 09 (2011) 045.
33. A. I. Davydychev, Phys. Lett. B PYLBAJ 0370-2693 10.1016/0370-2693(91) 91715-8 263, 107 (1991);
34. A. I. Davydychev, J. Phys. A JPHAC5 1361-6447 10.1088/0305-4470/25/21/017 25, 5587 (1992);
35. A. Bzowski, P. McFadden, and K. Skenderis, J. High Energy Phys. JHEPFG 1126-6708 10.1007/JHEP03(2012)091 03 (2012) 091.
36. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevB.87.085138 for the mathematica program "tjjcorr-scalar.nb" that automates the calculations in this paper. The Davydychev recursion relations are implemented in "Davydychev3.nb," using the code provided by P. McFadden. The answer produced by these relations is also simplified using the spinor-helicity formalism in this file.
37. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevB.87.085138 for the mathematica program "tjjcorr-fermion.nb" that automates the calculations in this paper.
38. S. Raju, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.85.126008 85, 126008 (2012).
39. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevB.87.085138 for the mathematica program "simplifybulk.nb" that automates the calculations in this paper.
40. S. Raju, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.85.126009 85, 126009 (2012).
41. J. Erdmenger and H. Osborn, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(96)00545-7 483, 431 (1997).
42. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevB.87.085138 for the mathematica program "energy-flux-d.nb" that automates the calculations in this paper. The supplemental calculations of certain position space correlators in d = four -, six-, and eight-dimensional CFTs are given in the mathematica programs "jtj-4d-position.nb," "jtj-6d-position.nb," and "jtj-8d-position.nb."
43. We thank J. Maldacena for discussions on these points.
44. A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.49.11919 49, 11919 (1994).
45. S. Sachdev, arXiv: 1012.0299.
46. K. Hanaki, K. Ohashi, and Y. Tachikawa, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.117.533 117, 533 (2007);
47. S. Cremonini, K. Hanaki, J. T. Liu, and P. Szepietowski, J. High Energy Phys. JHEPAB 1126-6708 10.1088/1126-6708/2009/12/045 12 (2009) 045.
48. R. C. Myers, M. F. Paulos, and A. Sinha, J. High Energy Phys. JHEPAB 1126-6708 10.1088/1126-6708/2009/06/006 06 (2009) 006.
49. A. Buchel and R. C. Myers, J. High Energy Phys. JHEPAB 1126-6708 10.1088/1126-6708/2009/08/016 08 (2009) 016;
50. M. Brigante, H. Liu, R. C. Myers, S. Shenker, and S. Yaida, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.191601 100, 191601 (2008). (Pubitemid 351705645)
51. R. C. Myers, A. O. Starinets, and R. M. Thomson, J. High Energy Phys. JHEPAB 1126-6708 10.1088/1126-6708/2007/11/091 11 (2007) 091;
52. M. Brigante, H. Liu, R. C. Myers, S. Shenker, and S. Yaida, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.77.126006 77, 126006 (2008).
53. D. Z. Freedman, S. D. Mathur, A. Matusis, and L. Rastelli, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(99)00053-X 546, 96 (1999).
54. O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y. Oz, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(99)00083-6 323, 183 (2000).
55. T. Banks, M. R. Douglas, G. T. Horowitz, and E. Martinec, arXiv: hep-th/9808016.
56. H. Liu and A. A. Tseytlin, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.59.086002 59, 086002 (1999).
57. S. M. Christensen and M. J. Duff, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(80)90423-X 170, 480 (1980);
58. S. Raju, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.83.126002 83, 126002 (2011).