Abstract
We consider excitations of LLM geometries described by coloring the LLM plane with concentric black rings. Certain closed string excitations are localized at the edges of these rings. The string theory predictions for the energies of magnon excitations of these strings depends on the radii of the edges of the rings. In this article we construct the operators dual to these closed string excitations and show how to reproduce the string theory predictions for magnon energies by computing one loop anomalous dimensions. These operators are linear combinations of restricted Schur polynomials. The distinction between what is the background and what is the excitation is accomplished in the choice of the subgroup and the representations used to construct the operator.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [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].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
N. Beisert, The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 948 [hep-th/0511082] [INSPIRE].
N. Beisert, The Analytic Bethe Ansatz for a Chain with Centrally Extended su(2—2) Symmetry, J. Stat. Mech. (2007) P01017 [nlin/0610017].
D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 super Yang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].
D. Berenstein, D.H. Correa and S.E. Vazquez, All loop BMN state energies from matrices, JHEP 02 (2006) 048 [hep-th/0509015] [INSPIRE].
D.M. Hofman and J.M. Maldacena, Giant Magnons, J. Phys. A 39 (2006) 13095 [hep-th/0604135] [INSPIRE].
J.H. Schwarz, Covariant Field Equations of Chiral N = 2 D = 10 Supergravity, Nucl. Phys. B 226 (1983) 269 [INSPIRE].
H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [INSPIRE].
D.M. Hofman and J.M. Maldacena, Reflecting magnons, JHEP 11 (2007) 063 [arXiv:0708.2272] [INSPIRE].
R. de Mello Koch, N.H. Tahiridimbisoa and C. Mathwin, Anomalous Dimensions of Heavy Operators from Magnon Energies, arXiv:1506.05224 [INSPIRE].
S. Corley, A. Jevicki and S. Ramgoolam, Exact correlators of giant gravitons from dual N = 4 SYM theory, Adv. Theor. Math. Phys. 5 (2002) 809[hep-th/0111222] [INSPIRE].
D. Berenstein, A toy model for the AdS/CFT correspondence, JHEP 07 (2004) 018 [hep-th/0403110] [INSPIRE].
J.A. Minahan and K. Zarembo, The Bethe-ansatz for N = 4 super Yang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [INSPIRE].
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
M. Kruczenski, Spin chains and string theory, Phys. Rev. Lett. 93 (2004) 161602 [hep-th/0311203] [INSPIRE].
V. Balasubramanian, M. Berkooz, A. Naqvi and M.J. Strassler, Giant gravitons in conformal field theory, JHEP 04 (2002) 034 [hep-th/0107119] [INSPIRE].
R. Bhattacharyya, S. Collins and R. de Mello Koch, Exact Multi-Matrix Correlators, JHEP 03 (2008) 044 [arXiv:0801.2061] [INSPIRE].
R. de Mello Koch, M. Dessein, D. Giataganas and C. Mathwin, Giant Graviton Oscillators, JHEP 10 (2011) 009 [arXiv:1108.2761] [INSPIRE].
T.W. Brown, P.J. Heslop and S. Ramgoolam, Diagonal multi-matrix correlators and BPS operators in N = 4 SYM, JHEP 02 (2008) 030 [arXiv:0711.0176] [INSPIRE].
T.W. Brown, P.J. Heslop and S. Ramgoolam, Diagonal free field matrix correlators, global symmetries and giant gravitons, JHEP 04 (2009) 089 [arXiv:0806.1911] [INSPIRE].
Y. Kimura and S. Ramgoolam, Branes, anti-branes and brauer algebras in gauge-gravity duality, JHEP 11 (2007) 078 [arXiv:0709.2158] [INSPIRE].
Y. Kimura, Non-holomorphic multi-matrix gauge invariant operators based on Brauer algebra, JHEP 12 (2009) 044 [arXiv:0910.2170] [INSPIRE].
Y. Kimura, Correlation functions and representation bases in free N = 4 Super Yang-Mills, Nucl. Phys. B 865 (2012) 568 [arXiv:1206.4844] [INSPIRE].
J. Pasukonis and S. Ramgoolam, Quivers as Calculators: Counting, Correlators and Riemann Surfaces, JHEP 04 (2013) 094 [arXiv:1301.1980] [INSPIRE].
R. de Mello Koch, J. Smolic and M. Smolic, Giant Gravitons — with Strings Attached (I), JHEP 06 (2007) 074 [hep-th/0701066] [INSPIRE].
R. Bhattacharyya, R. de Mello Koch and M. Stephanou, Exact Multi-Restricted Schur Polynomial Correlators, JHEP 06 (2008) 101 [arXiv:0805.3025] [INSPIRE].
N. Beisert, C. Kristjansen and M. Staudacher, The dilatation operator of conformal N = 4 super Yang-Mills theory, Nucl. Phys. B 664 (2003) 131 [hep-th/0303060] [INSPIRE].
V. De Comarmond, R. de Mello Koch and K. Jefferies, Surprisingly Simple Spectra, JHEP 02 (2011) 006 [arXiv:1012.3884] [INSPIRE].
R. de Mello Koch, Geometries from Young Diagrams, JHEP 11 (2008) 061 [arXiv:0806.0685] [INSPIRE].
R. de Mello Koch, N. Ives and M. Stephanou, Correlators in Nontrivial Backgrounds, Phys. Rev. D 79 (2009) 026004 [arXiv:0810.4041] [INSPIRE].
R. de Mello Koch, T.K. Dey, N. Ives and M. Stephanou, Correlators of operators with a large R-charge, JHEP 08 (2009) 083 [arXiv:0905.2273] [INSPIRE].
D. Berenstein, Large-N BPS states and emergent quantum gravity, JHEP 01 (2006) 125 [hep-th/0507203] [INSPIRE].
S.E. Vazquez, Reconstructing 1/2 BPS Space-Time Metrics from Matrix Models and Spin Chains, Phys. Rev. D 75 (2007) 125012 [hep-th/0612014] [INSPIRE].
H.-Y. Chen, D.H. Correa and G.A. Silva, Geometry and topology of bubble solutions from gauge theory, Phys. Rev. D 76 (2007) 026003 [hep-th/0703068] [INSPIRE].
H. Lin, A. Morisse and J.P. Shock, Strings on Bubbling Geometries, JHEP 06 (2010) 055 [arXiv:1003.4190] [INSPIRE].
D. Berenstein, Giant gravitons: a collective coordinate approach, Phys. Rev. D 87 (2013) 126009 [arXiv:1301.3519] [INSPIRE].
D. Berenstein and E. Dzienkowski, Open spin chains for giant gravitons and relativity, JHEP 08 (2013) 047 [arXiv:1305.2394] [INSPIRE].
D. Berenstein, Sketches of emergent geometry in the gauge/gravity duality, Fortsch. Phys. 62 (2014) 776 [arXiv:1404.7052] [INSPIRE].
D. Berenstein and E. Dzienkowski, Giant gravitons and the emergence of geometric limits in β-deformations of \( \mathcal{N}=4 \) SYM, JHEP 01 (2015) 126 [arXiv:1408.3620] [INSPIRE].
D. Berenstein, On the central charge extension of the \( \mathcal{N}=4 \) SYM spin chain, JHEP 05 (2015) 129 [arXiv:1411.5921] [INSPIRE].
M. Hamermesh, Group Theory and its Application to Physical Problems, Addison-Wesley Publishing Company Inc., New York U.S.A. (1962).
W. Carlson, R. de Mello Koch and H. Lin, Nonplanar Integrability, JHEP 03 (2011) 105 [arXiv:1101.5404] [INSPIRE].
N.R. Constable et al., PP wave string interactions from perturbative Yang-Mills theory, JHEP 07 (2002) 017 [hep-th/0205089] [INSPIRE].
R. de Mello Koch, T.K. Dey, N. Ives and M. Stephanou, Hints of Integrability Beyond the Planar Limit: Nontrivial Backgrounds, JHEP 01 (2010) 014 [arXiv:0911.0967] [INSPIRE].
N. Dorey, Magnon Bound States and the AdS/CFT Correspondence, J. Phys. A 39 (2006) 13119 [hep-th/0604175] [INSPIRE].
V. Balasubramanian, D. Berenstein, B. Feng and M.-x. Huang, D-branes in Yang-Mills theory and emergent gauge symmetry, JHEP 03 (2005) 006 [hep-th/0411205] [INSPIRE].
R. de Mello Koch, J. Smolic and M. Smolic, Giant Gravitons — with Strings Attached (II), JHEP 09 (2007) 049 [hep-th/0701067] [INSPIRE].
D. Bekker, R. de Mello Koch and M. Stephanou, Giant Gravitons — with Strings Attached. III., JHEP 02 (2008) 029 [arXiv:0710.5372] [INSPIRE].
V. Balasubramanian, J. de Boer, V. Jejjala and J. Simon, The Library of Babel: On the origin of gravitational thermodynamics, JHEP 12 (2005) 006 [hep-th/0508023] [INSPIRE].
M. Dodelson and E. Silverstein, String-theoretic breakdown of effective field theory near black hole horizons, arXiv:1504.05536 [INSPIRE].
R. de Mello Koch and R. Gwyn, Giant graviton correlators from dual SU(N) super Yang-Mills theory, JHEP 11 (2004) 081 [hep-th/0410236] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1601.06914
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
de Mello Koch, R., Mathwin, C. & van Zyl, H.J.R. LLM magnons. J. High Energ. Phys. 2016, 110 (2016). https://doi.org/10.1007/JHEP03(2016)110
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2016)110