Review of AdS/CFT Integrability, Chapter IV.3: N = 4 6 Chern-Simons and Strings on AdS 4 × CP 3

Letters in Mathematical Physics

Volumn 99, Issue 1-3, 2012, Pages 401-423

  Klose, Thomas ^a  

^a UPPSALA UNIVERSITY   (Sweden)

Author keywords

AdS CFT correspondence; integrability; superconformal Chern Simons theory; superstrings on Ads 4 CP 3

Indexed keywords

EID: 84856233108     PISSN: 03779017     EISSN: 15730530     Source Type: Journal    
DOI: 10.1007/s11005-011-0520-y     Document Type: Review

References (93)

1. Beisert, N., et al.: Review of AdS/CFT integrability: an overview. Lett. Math. Phys. Published in this volume. arxiv: 1012. 3982.
2. Aharony O., Bergman O., Jafferis D. L., Maldacena J. (2008) N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals. JHEP 0810: 091. doi: 10. 1088/1126-6708/2008/10/091 (arxivref: 0806. 1218).
3. Babichenko A., Stefański B. Jr., Zarembo K. (2010) Integrability and the AdS(3)/CFT(2) correspondence. JHEP 1003: 058. doi: 10. 1007/JHEP03(2010)058 (arxiv: 0912. 1723).
4. 3. JHEP 0907: 016. doi: 10. 1088/1126-6708/2009/07/016 (arxiv: 0902. 1743).
5. Klebanov I. R., Torri G. (2010) M2-branes and AdS/CFT. Int. J. Mod. Phys. A 25: 332. doi: 10. 1142/S0217751X10048652 (arxiv: 0909. 1580).
6. Klose, T., McLoughlin, T.: Integrability in Ads4/CFT3 (in preparation).
7. Beisert N. (2008) The su(2/2) dynamic S-matrix. Adv. Theor. Math. Phys. 12: 945 hep-th/0511082.
8. Berenstein D., Trancanelli D. (2008) Three-dimensional N = 4 SCFT's and their membrane dynamics. Phys. Rev. D 78: 106009. doi: 10. 1103/PhysRevD. 78. 106009 (arxiv: 0808. 2503).
9. Berenstein, D., Trancanelli, D.: S-duality and the giant magnon dispersion relation. arxiv: 0904. 0444.
10. Minahan J. A., Zarembo K. (2008) The Bethe ansatz for superconformal Chern-Simons. JHEP 0809: 040. doi: 10. 1088/1126-6708/2008/09/040 (arxiv: 0806. 3951).
11. Gaiotto D., Giombi S., Yin X. (2009) Spin Chains in N = 4 superconformal Chern- Simons-matter. Theory JHEP 0904: 066. doi: 10. 1088/1126-6708/2009/04/066 (arxiv: 0806. 4589).
12. Grignani G., Harmark T., Orselli M. (2009) The SU(2) × SU(2) sector in the string dual of N = 4 superconformal Chern-Simons theory. Nucl. Phys. B 810: 115. doi: 10. 1016/j. nuclphysb. 2008. 10. 019 (arxiv: 0806. 4959).
13. 3: testing the Bethe Ansatz proposal. JHEP 0811: 069. doi: 10. 1088/1126-6708/2008/11/069 (arxiv: 0809. 4038).
14. Shenderovich, I.: Giant magnons in Ads4/CFT3: dispersion, quantization and finite-size corrections. arxiv: 0807. 2861.
15. 4/CFT3 Bethe ansatz. JHEP 0901: 016. doi: 10. 1088/1126-6708/2009/01/016 (arxiv: 0807. 0777).
16. Bandres M. A., Lipstein A. E., Schwarz J. H. (2008) Studies of the ABJM theory in a formulation with manifest SU(4) R-Symmetry. JHEP 0809: 027. doi: 10. 1088/1126-6708/2008/09/027 (arxiv: 0807. 0880).
17. Papathanasiou G., Spradlin M. (2009) The Morphology of N = 4 Chern-Simons theory. JHEP 0907: 036. doi: 10. 1088/1126-6708/2009/07/036 (arxiv: 0903. 2548).
18. 3 correspondence. JHEP 0809: 072. doi: 10. 1088/1126-6708/2008/09/072 (arxiv: 0806. 1519).
19. Buchbinder I. L. et al (2009) ABJM models in N = 3 harmonic superspace. JHEP 0903: 096. doi: 10. 1088/1126-6708/2009/03/096 (arxiv: 0811. 4774).
20. Mauri A., Petkou A. C. (2008) An N = 4 1 superfield action for M2 branes. Phys. Lett. B 666: 527. doi: 10. 1016/j. physletb. 2008. 07. 098 (arxiv: 0806. 2270).
21. Cederwall M. (2008) Superfield actions forN = 4 conformal theories in three dimensions. JHEP 0810: 070. doi: 10. 1088/1126-6708/2008/10/070 (arxiv: 0809. 0318).
22. Bak D., Rey S.-J. (2008) Integrable spin chain in superconformal Chern-Simons theory. JHEP 0810: 053. doi: 10. 1088/1126-6708/2008/10/053 (arxiv: 0807. 2063).
23. Aharony O., Bergman O., Jafferis D. L. (2008) Fractional M2-branes. JHEP 0811: 043. doi: 10. 1088/1126-6708/2008/11/043 (arxiv: 0807. 4924).
24. Gaiotto D., Tomasiello A. (2010) The gauge dual of Romans mass. JHEP 1001: 015. doi: 10. 1007/JHEP01(2010)015 (arxiv: 0901. 0969).
25. Forcella, D., Schulgin, W.: Spin chain for the deformed ABJM theory. arxiv: 0906. 3301).
26. Zwiebel, B. I.: Two-loop integrability of planar N = 4 superconformal Chern-Simons theory. arxiv: 0901. 0411.
27. Beccaria M., Macorini G. (2009) QCD properties of twist operators in the N = 4 Chern-Simons theory. JHEP 0906: 008. doi: 10. 1088/1126-6708/2009/06/008 (arxiv: 0904. 2463).
28. Beccaria, M., Macorini, G.: The virtual scaling function of twist operators in the N = 4 Chern-Simons theory. arxiv: 0905. 1030.
29. Minahan J. A., Schulgin W., Zarembo K. (2009) Two loop integrability for Chern-Simons theories with N = 4 supersymmetry. JHEP 0903: 057. doi: 10. 1088/1126-6708/2009/03/057 (arxiv: 0901. 1142).
30. Bak D., Gang D., Rey S.-J. (2008) Integrable spin chain of superconformal U(M)xU(N) Chern-Simons theory. JHEP 0810: 038. doi: 10. 1088/1126-6708/2008/10/038 (arxiv: 0808. 0170).
31. Minahan J. A., Ohlsson Sax O., Sieg C. (2010) Magnon dispersion to four loops in the ABJM and ABJ models. J. Phys. A 43: 275402. doi: 10. 1088/1751-8113/43/27/275402 (arxiv: 0908. 2463).
32. Minahan, J. A., Ohlsson Sax, O., Sieg, C.: Anomalous dimensions at four loops in N = 4 6 superconformal Chern-Simons theories. arxiv: 0912. 3460.
33. Leoni M., Mauri A., Minahan J., Ohlsson Sax O., Santambrogio A., Sieg C., Tartaglino-Mazzucchelli G. (2010) Superspace calculation of the four-loop spectrum in N = 4 6 supersymmetric Chern-Simons theories. JHEP 1012: 074. doi: 10. 1007/JHEP12(2010)074 (arxiv: 1010. 1756).
34. Minahan, J. A., Ohlsson Sax, O., Sieg, C.: A limit on the ABJ model. arxiv: 1005. 1786.
35. Bak, D., Min, H., Rey, S.-J.: Integrability of N = 4 6 Chern-Simons theory at six loops and beyond. arxiv: 0911. 0689.
36. Kristjansen C., Orselli M., Zoubos K. (2009) Non-planar ABJM theory and integrability. JHEP 0903: 037. doi: 10. 1088/1126-6708/2009/03/037 (arxiv: 0811. 2150).
37. Caputa P., Kristjansen C., Zoubos K. (2009) Non-planar ABJ theory and parity. Phys. Lett. B 677: 197. doi: 10. 1016/j. physletb. 2009. 05. 021 (arxiv: 0903. 3354).
38. Nilsson B. E. W., Pope C. N. (1984) Hopf fibration of eleven-dimensional supergravity. Class. Quant. Grav. 1: 499. doi: 10. 1088/0264-9381/1/5/005.
39. 3 superspace for the type IIA superstring and D-branes. JHEP 0903: 015. doi: 10. 1088/1126-6708/2009/03/015 (arxiv: 0811. 1566).
40. Grisaru M. T., Howe P. S., Mezincescu L., Nilsson B., Townsend P. K. (1985) N = 4 2 superstrings in a supergravity background. Phys. Lett. B 162: 116. doi: 10. 1016/0370-2693(85)91071-8.
41. 3 superbackground. JHEP 0908: 060. doi: 10. 1088/1126-6708/2009/08/060 (arxiv: 0903. 5407).
42. 3 as a coset sigma-model. JHEP 0809: 129. doi: 10. 1088/1126-6708/2008/09/129 (arxiv: 0806. 4940).
43. 3. Nucl. Phys. B 808: 80. doi: 10. 1016/j. nuclphysb. 2008. 09. 015 (arxiv: 0806. 4948).
44. 5 background. Nucl. Phys. B 533: 109. doi: 10. 1016/S0550-3213(98)00570-7 (hep-th/9805028).
45. Henneaux M., Mezincescu L. (1985) A sigma model interpretation of Green-Schwarz covariant superstring action. Phys. Lett. B 152: 340. doi: 10. 1016/0370-2693(85)90507-6.
46. 2 as a coset supermanifold. Nucl. Phys. B 567: 61. doi: 10. 1016/S0550-3213(99)00683-5 (hep-th/9907200).
47. 3 superstring and D = 3 N = 6 superconformal symmetry. Phys. Rev. D 79: 106007. doi: 10. 1103/PhysRevD. 79. 106007 (arxiv: 0811. 2813).
48. Zarembo, K.: Worldsheet spectrum in Ads4/CFT3 correspondence. arxiv: 0903. 1747.
49. Nishioka T., Takayanagi T. (2008) On type IIA penrose limit and N = 4 Chern-Simons theories. JHEP 0808: 001. doi: 10. 1088/1126-6708/2008/08/001 (arxiv: 0806. 3391).
50. 3 in a near plane wave limit. arxiv: 0912. 2257.
51. Grignani, G., Harmark, T., Marini, A., Orselli, M.: New penrose limits and AdS/CFT. arxiv: 0912. 5522.
52. 3. Nucl. Phys. B 810: 150. doi: 10. 1016/j. nuclphysb. 2008. 10. 020 (arxiv: 0807. 1527).
53. 3 string and its Bethe equations in the near plane wave limit. JHEP 0902: 046. doi: 10. 1088/1126-6708/2009/02/046 (arxiv: 0811. 2775).
54. 3 superstring. arxiv: 0909. 0697.
55. Fre, P., Grassi, P. A.: Pure spinor formalism for Osp(N/4) backgrounds. arxiv: 0807. 0044.
56. 3. JHEP 0810: 085. doi: 10. 1088/1126-6708/2008/10/085 (arxiv: 0808. 1051).
57. 3 from supergravity. Phys. Rev. D 79: 086001 arxiv: 0808. 1282.
58. 3 superstring in the light-cone gauge. Nucl. Phys. B 826: 294. doi: 10. 1016/j. nuclphysb. 2009. 10. 006 (arxiv: 0906. 4699).
59. Abdalla E., Forger M., Gomes M. (1982) On the origin of anomalies in the quantum non-local charge for the generalized non-linear sigma models. Nucl. Phys. B 210: 181. doi: 10. 1016/0550-3213(82)90238-3.
60. Abdalla E., Forger M., Lima Santos A. (1985) Non-local charges for non-linear sigma models on Grassmann manifolds. Nucl. Phys. B 256: 145. doi: 10. 1016/0550-3213(85)90389-X.
61. 5 superstring. Phys. Rev. D 69: 046002. doi: 10. 1103/PhysRevD. 69. 046002 (hep-th/0305116).
62. 3. arxiv: 0905. 4702.
63. 3. JHEP 0809: 017. doi: 10. 1088/1126-6708/2008/09/017 (arxiv: 0807. 3134).
64. 3 string sigma model. Phys. Rev. D 78: 106012. doi: 10. 1103/PhysRevD. 78. 106012 (arxiv: 0808. 3057).
65. 3 superstring. Phys. Rev. D 80: 046005. doi: 10. 1103/PhysRevD. 80. 046005 (arxiv: 0906. 0706).
66. 3 superstring. arxiv: 0904. 0208.
67. Hofman D. M., Maldacena J. M. (2006) Giant magnons. J. Phys. A 39: 13095. doi: 10. 1088/0305-4470/39/41/S17 (hep-th/0604135).
68. Dorey N. (2006) Magnon bound states and the AdS/CFT correspondence. J. Phys. A 39: 13119. doi: 10. 1088/0305-4470/39/41/S18 (hep-th/0604175).
69. Chen H.-Y., Dorey N., Okamura K. (2006) Dyonic giant magnons. JHEP 0609: 024. doi: 10. 1088/1126-6708/2006/09/024 (hep-th/0605155).
70. 3: embeddings, charges and a Hamiltonian. arxiv: 0811. 2423.
71. 3: strings and curves at finite. J. Phys. Rev. D 80: 026005. doi: 10. 1103/PhysRevD. 80. 026005 (arxiv: 0903. 3365).
72. n dyonic magnon. arxiv: 0905. 2534.
73. 3. JHEP 1002: 085. doi: 10. 1007/JHEP02(2010)085 (arxiv: 0910. 5315).
74. Ahn C., Nepomechie R. I. (2008) N = 4 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations. JHEP 0809: 010. doi: 10. 1088/1126-6708/2008/09/010 (arxiv: 0807. 1924).
75. n. arxiv: 1005. 1066.
76. Hollowood T. J., Miramontes J. L. (2009) Magnons, their solitonic avatars and the Pohlmeyer reduction. JHEP 0904: 060. doi: 10. 1088/1126-6708/2009/04/060 (arxiv: 0902. 2405).
77. 3. JHEP 0907: 006. doi: 10. 1088/1126-6708/2009/07/006 (arxiv: 0902. 3179).
78. 3 by dressing method. JHEP 0905: 079. doi: 10. 1088/1126-6708/2009/05/079 (arxiv: 0902. 3368).
79. Staudacher, M.: Review of AdS/CFT integrability, chapter III. 1: Bethe Ansätze and the R-matrix formalism. Lett. Math. Phys. Published in this volume. arxiv: 1012. 3990.
80. Ahn, C., Nepomechie, R. I.: Review of AdS/CFT integrability, chapter III. 2: exact world-sheet S-matrix. Lett. Math. Phys. Published in this volume. arxiv: 1012. 3991.
81. Schafer-Nameki, S.: Review of AdS/CFT integrability, chapter II. 4: the spectral curve. Lett. Math. Phys. Published in this volume. arxiv: 1012. 3989.
82. Bajnok, Z.: Review of AdS/CFT integrability, chapter III. 6: thermodynamic Bethe Ansatz. Lett. Math. Phys. Published in this volume. arxiv: 1012. 3995.
83. Kazakov, V., Gromov, N.: Review of AdS/CFT integrability, chapter III. 7: Hirota dynamics for quantum integrability. Lett. Math. Phys. Published in this volume. arxiv: 1012. 3996.
84. Papathanasiou, G., Spradlin, M.: Two-loop spectroscopy of short ABJM operators. JHEP 1002, 072 (2010). 10. 1007/JHEP02(2010)072 (arxiv: 0911. 2220).
85. 5 superstring. JHEP 0704, 002 (2007). 10. 1088/1126-6708/2007/04/002 (hep-th/0612229).
86. Beisert N., Eden B., Staudacher M. (2007) Transcendentality and crossing. J. Stat. Mech. 0701: P021 hep-th/0610251.
87. Ahn C., Nepomechie R. I. (2009) An alternative S-matrix for N = 4 Chern-Simons theory?. JHEP 0903: 068. doi: 10. 1088/1126-6708/2009/03/068 (arxiv: 0810. 1915).
88. Ahn C., Nepomechie R. I. (2009) Two-loop test of the N = 4 Chern-Simons theory S-matrix. JHEP 0903: 144. doi: 10. 1088/1126-6708/2009/03/144 (arxiv: 0901. 3334).
89. Ahn, C., Dorey, P., Nepomechie, R. I.: On the absence of reflection in AdS4/CFT3. arxiv: 0910. 5584.
90. 4/CFT3 algebraic curve. JHEP 0902: 040. doi: 10. 1088/1126-6708/2009/02/040 (arxiv: 0807. 0437).
91. Gromov, N., Kazakov, V., Vieira, P.: Integrability for the full spectrum of planar AdS/CFT. arxiv: 0901. 3753.
92. Bombardelli, D., Fioravanti, D., Tateo, R.: TBA and Y-system for planar AdS4/CFT3. Nucl. Phys. B 834, 543 (2010). 10. 1016/j. nuclphysb. 2010. 04. 005 (arxiv: 0912. 4715).
93. Gromov, N., Levkovich-Maslyuk, F.: Y-system, TBA and quasi-classical strings in AdS4 × CP3. arxiv: 0912. 4911.