Geodesic
Limiting Cases of a Superstring in ${AdS}_5 \times {S}^5$
Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 1, pp. 69-86
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The superstring action in ${AdS}_5 \times {S}^5$ depends on two parameters: the inverse string tension $\alpha '$ and the radius $R$. The “standard” AdS/CFT correspondence requires that the string action depend on only the combination $\sqrt \lambda = R^2/\alpha '$. After reviewing previous work on the light-cone superstring, we derive the explicit form of the action $\lambda = 0$. Its zero-mode part coincides with the superparticle action in {${AdS}_5 \times {S}^5$}, and the $\lambda =0$ string spectrum, as expected, must therefore include the “protected” type-IIB supergravity states. Following recent suggestions, we conjecture that such a tensionless string spectrum must also contain higher-spin massless states in $AdS_5$. We also discuss the case of another parameterization of the string action that admits the straightforward flat-space limit $R\to \infty $, but the limits $R \to 0 $ and $\alpha ' \to \infty $ are not equivalent in this case. The limit $R \to 0$ then corresponds to shrinking $S^5$ to the size zero, simultaneously “freezing” the fluctuations of the radial coordinate of $AdS_5$. This case results in a “nonstandard” AdS/CFT correspondence picture.
Keywords: superstring in the light-cone gauge, low-energy limit, effective action, AdS/CFT correspondence. 
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A. A. Tseytlin. Limiting Cases of a Superstring in ${AdS}_5 \times {S}^5$. Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 1, pp. 69-86. http://geodesic.mathdoc.fr/item/TMF_2002_133_1_a4/

[1] J. Maldacena, Adv. Theor. Math. Phys., 2 (1998), 231 ; ; S. S. Gubser, I. R. Klebanov, A. M. Polyakov, Phys. Lett. B, 428 (1998), 105 ; ; E. Witten, Adv. Theor. Math. Phys., 2 (1998), 253 ; E-print hep-th/9711200E-print hep-th/9802109E-print hep-th/9802150 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[2] R. R. Metsaev, A. A. Tseytlin, Phys. Rev. D, 63 (2001), 046002 ; E-print hep-th/0007036 | DOI | MR

[3] R. R. Metsaev, C. B. Thorn, A. A. Tseytlin, Nucl. Phys. B, 596 (2001), 151 ; E-print hep-th/0009171 | DOI | MR | Zbl

[4] M. B. Green, J. H. Schwarz, Phys. Lett. B, 109 (1982), 444 | DOI

[5] R. R. Metsaev, Phys. Lett. B, 468 (1999), 65 ; E-print hep-th/9908114 | DOI | MR | Zbl

[6] U. Lindstrom, B. Sundborg, G. Theodoridis, Phys. Lett. B, 253 (1991), 319 ; J. Isberg, U. Lindstrom, B. Sundborg, Phys. Lett. B, 293 (1992), 321 ; ; J. Isberg, U. Lindstrom, B. Sundborg, G. Theodoridis, Nucl. Phys. B, 411 (1994), 122 ; E-print hep-th/9207005E-print hep-th/9307108 | DOI | MR | DOI | MR | DOI | MR | Zbl

[7] B. Sundborg, Nucl. Phys. Proc. Suppl., 102 (2001), 113 ; ; P. Haggi-Mani, B. Sundborg, JHEP, 0004 (2000), 031 ; E-print hep-th/0103247E-print hep-th/0002189 | DOI | MR | Zbl | DOI | MR

[8] E. Witten, Talk at J. H. Schwarz 60-th Birthday Conference (CalTech, November 2–3, 2001)

[9] M. A. Vasiliev, Conformal higher spin symmetries of 4D massless supermultiplets and $osp(L,2M)$ invariant equations in generalized (super)space, ; Nucl. Phys. B, 616 (2001), 106 ; E-print hep-th/0106149E-print hep-th/0106200 | MR | DOI | MR | Zbl

[10] E. Sezgin, P. Sundell, JHEP, 0109 (2001), 025 ; ; JHEP, 0109 (2001), 036 ; E-print hep-th/0107186E-print hep-th/0105001 | DOI | MR | DOI | MR

[11] A. Mikhailov, Notes on higher spin symmetries, E-print hep-th/0201019

[12] S. E. Konstein, M. A. Vasiliev, V. N. Zaikin, JHEP, 0012 (2000), 018 ; ; D. Anselmi, Nucl. Phys. B, 541 (1999), 323 ; ; Class. Q Grav., 17 (2000), 1383 ; E-print hep-th/0010239E-print hep-th/9808004E-print hep-th/9906167 | DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl

[13] H. Nastase, W. Siegel, JHEP, 0010 (2000), 040 ; E-print hep-th/0010106 | DOI | MR

[14] H. Liu, A. A. Tseytlin, Nucl. Phys. B, 533 (1998), 88 ; E-print hep-th/9804083 | DOI | MR | Zbl

[15] R. R. Metsaev, Nucl. Phys. B, 563 (1999), 295 ; E-print hep-th/9906217 | DOI | MR | Zbl

[16] R. R. Metsaev, Light-cone form of field dynamics in $AdS$ space-time, E-print hep-th/0011112 | MR

[17] N. Boulanger, M. Henneaux, P. van Nieuwenhuizen, Conformal (super)gravities with several gravitons, E-print hep-th/0201023

[18] E. S. Fradkin, A. A. Tseytlin, Phys. Rep., 119 (1985), 233 | DOI | MR

[19] M. Kaku, P. K. Townsend, P. van Nieuwenhuizen, Phys. Rev. D, 17 (1978), 3179 | DOI | MR

[20] E. S. Fradkin, V. Y. Linetsky, Mod. Phys. Lett. A, 4 (1989), 731 ; Ann. Phys., 198 (1990), 293 | DOI | MR | Zbl | DOI | MR | Zbl

[21] E. S. Fradkin, V. Y. Linetsky, Phys. Lett. B, 231 (1989), 97 ; Nucl. Phys. B, 350 (1991), 274 | DOI | MR | Zbl | DOI | MR

[22] E. S. Fradkin, A. A. Tseytlin, Phys. Lett. B, 134 (1984), 187 | DOI | MR | Zbl

[23] R. R. Metsaev, A. A. Tseytlin, Nucl. Phys. B, 533 (1998), 109 ; E-print hep-th/9805028 | DOI | MR | Zbl

[24] I. Pesando, JHEP, 9811 (1998), 002 ; ; Mod. Phys. Lett. A, 14 (1999), 343 ; E-print hep-th/9808020E-print hep-th/9808146 | DOI | MR | DOI | MR

[25] R. Kallosh, J. Rahmfeld, Phys. Lett. B, 443 (1998), 143 ; ; R. Kallosh, A. A. Tseytlin, JHEP, 10 (1998), 016 ; E-print hep-th/9808038E-print hep-th/9808088 | DOI | MR | DOI | MR | Zbl

[26] R. Roiban, W. Siegel, JHEP, 0011 (2000), 024 ; E-print hep-th/0010104 | DOI | MR

[27] R. Kallosh, A. Rajaraman, Phys. Rev. D, 58 (1998), 125003 ; E-print hep-th/9805041 | DOI | MR

[28] A. M. Polyakov, Gauge fields and space-time, E-print hep-th/0110196 | MR

[29] A. A. Tseytlin, Int. J. Mod. Phys. A, 16 (2001), 900 ; E-print hep-th/0009226 | DOI | MR | Zbl

[30] A. M. Polyakov, Private communication, 2000

[31] J. Polchinski, L. Susskind, String theory and the size of hadrons, E-print hep-th/0112204

[32] P. Goddard, J. Goldstone, C. Rebbi, C. B. Thorn, Nucl. Phys. B, 56 (1973), 109 | DOI

[33] N. Drukker, D. J. Gross, A. A. Tseytlin, JHEP, 0004 (2000), 021 ; E-print hep-th/0001204 | DOI | MR