Abstract
We propose a new entry within the dictionary of the AdS/CFT duality at strong coupling: in the limit of a large spin or a large R-charge, the anomalous dimension of the gauge theory operator dual to a semiclassical rotating string is proportional to the string proper length. This conjecture is motivated by a generalization to strings of the rule for computing anomalous dimensions of massive particles and supergravity fields in the anti-de Sitter space. We show that this proportionality holds for a rotating closed string in global AdS space, representing a high spin operator made of fields in the adjoint representation. It is also valid for closed strings rotating in S 5 (representing operators with large R-charge), for closed strings with multiple AdS spin, and for giant magnons. Based on this conjecture, we calculate the anomalous dimension δ of operators made of fields in the fundamental representation, associated with high spin mesons, and which are represented by rotating open strings attached to probe D7-branes. The result is a logarithmic dependence upon the spin, \( \delta \sim \sqrt{\uplambda} \ln\;S \), similar to the closed string case. We show that the operator properties — anomalous dimension and spin — are obtained from measurements made by a local observer in the anti-de Sitter space. For the open string case, this ensures that these quantities are independent of the mass scale introduced by the D7-branes (the quark mass), as expected on physical grounds. In contrast, properties of the gauge theory states, like the energy, correspond to measurements by a gauge theory observer and depend upon the mass scale — once again, as expected.
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References
D.J. Gross and F. Wilczek, Asymptotically free gauge theories. 2, Phys. Rev. D 9 (1974) 980 [INSPIRE].
H. Georgi and H.D. Politzer, Electroproduction scaling in an asymptotically free theory of strong interactions, Phys. Rev. D 9 (1974) 416 [INSPIRE].
G.P. Korchemsky, Asymptotics of the Altarelli-Parisi-Lipatov evolution kernels of parton distributions, Mod. Phys. Lett. A 4 (1989) 1257 [INSPIRE].
G.P. Korchemsky and G. Marchesini, Structure function for large x and renormalization of Wilson loop, Nucl. Phys. B 406 (1993) 225 [hep-ph/9210281] [INSPIRE].
B. Basso and G.P. Korchemsky, Anomalous dimensions of high-spin operators beyond the leading order, Nucl. Phys. B 775 (2007) 1 [hep-th/0612247] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, A Semiclassical limit of the gauge/string correspondence, Nucl. Phys. B 636 (2002) 99 [hep-th/0204051] [INSPIRE].
N. Drukker, D.J. Gross and H. Ooguri, Wilson loops and minimal surfaces, Phys. Rev. D 60 (1999) 125006 [hep-th/9904191] [INSPIRE].
M. Kruczenski, A note on twist two operators in N = 4 SYM and Wilson loops in Minkowski signature, JHEP 12 (2002) 024 [hep-th/0210115] [INSPIRE].
Y. Makeenko, Light cone Wilson loops and the string/gauge correspondence, JHEP 01 (2003) 007 [hep-th/0210256] [INSPIRE].
A.V. Belitsky, A.S. Gorsky and G.P. Korchemsky, Gauge/string duality for QCD conformal operators, Nucl. Phys. B 667 (2003) 3 [hep-th/0304028] [INSPIRE].
M. Kruczenski, R. Roiban, A. Tirziu and A.A. Tseytlin, Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS 5 × S 5, Nucl. Phys. B 791 (2008) 93 [arXiv:0707.4254] [INSPIRE].
L.F. Alday and J.M. Maldacena, Comments on operators with large spin, JHEP 11 (2007) 019 [arXiv:0708.0672] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
M. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Meson spectroscopy in AdS/CFT with flavor, JHEP 07 (2003) 049 [hep-th/0304032] [INSPIRE].
J. Erdmenger, N. Evans, I. Kirsch and E. Threlfall, Mesons in gauge/gravity duals — A review, Eur. Phys. J. A 35 (2008) 81 [arXiv:0711.4467] [INSPIRE].
R.A. Janik, P. Surowka and A. Wereszczynski, On correlation functions of operators dual to classical spinning string states, JHEP 05 (2010) 030 [arXiv:1002.4613] [INSPIRE].
S. Frolov and A.A. Tseytlin, Multispin string solutions in AdS 5 × S 5, Nucl. Phys. B 668 (2003) 77 [hep-th/0304255] [INSPIRE].
D.M. Hofman and J.M. Maldacena, Giant magnons, J. Phys. A 39 (2006) 13095 [hep-th/0604135] [INSPIRE].
M.K. Benna, S. Benvenuti, I.R. Klebanov and A. Scardicchio, A test of the AdS/CFT correspondence using high-spin operators, Phys. Rev. Lett. 98 (2007) 131603 [hep-th/0611135] [INSPIRE].
J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].
S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large-N gauge theory and Anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [INSPIRE].
H. Boschi-Filho and N.R.F. Braga, Isometries of a D3-brane space, Class. Quant. Grav. 21 (2004) 2427 [hep-th/0311012] [INSPIRE].
D.E. Berenstein, E. Gava, J.M. Maldacena, K.S. Narain and H.S. Nastase, Open strings on plane waves and their Yang-Mills duals, hep-th/0203249 [INSPIRE].
B. Stefanski Jr., Open spinning strings, JHEP 03 (2004) 057 [hep-th/0312091] [INSPIRE].
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Braga, N.R.F., Iancu, E. Anomalous dimensions from rotating open strings in AdS/CFT. J. High Energ. Phys. 2014, 104 (2014). https://doi.org/10.1007/JHEP08(2014)104
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DOI: https://doi.org/10.1007/JHEP08(2014)104