Abstract
We study the spectrum of anomalous dimensions of operators dual to giant graviton branes. The operators considered belong to the su(2|3) sector of \( \mathcal{N} \) = 4 super Yang-Mills theory, have a bare dimension ∼ N and are a linear combination of restricted Schur polynomials with p ∼ O(1) long rows or columns. In the same way that the operator mixing problem in the planar limit can be mapped to an integrable spin chain, we find that our problems maps to particles hopping on a lattice. The detailed form of the model is in precise agreement with the expected world volume dynamics of p giant graviton branes, which is a U(p) Yang-Mills theory. The lattice model we find has a number of noteworthy features. It is a lattice model with all-to-all sites interactions and quenched disorder.
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References
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [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].
J. McGreevy, L. Susskind and N. Toumbas, Invasion of the giant gravitons from Anti-de Sitter space, JHEP 06 (2000) 008 [hep-th/0003075] [INSPIRE].
M.T. Grisaru, R.C. Myers and O. Tafjord, SUSY and goliath, JHEP 08 (2000) 040 [hep-th/0008015] [INSPIRE].
A. Hashimoto, S. Hirano and N. Itzhaki, Large branes in AdS and their field theory dual, JHEP 08 (2000) 051 [hep-th/0008016] [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].
V. Balasubramanian, M. Berkooz, A. Naqvi and M.J. Strassler, Giant gravitons in conformal field theory, JHEP 04 (2002) 034 [hep-th/0107119] [INSPIRE].
N. Beisert, The complete one loop dilatation operator of N = 4 superYang-Mills theory, Nucl. Phys. B 676 (2004) 3 [hep-th/0307015] [INSPIRE].
R. de Mello Koch and S. Ramgoolam, A double coset ansatz for integrability in AdS/CFT, JHEP 06 (2012) 083 [arXiv:1204.2153] [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 (I), JHEP 06 (2007) 074 [hep-th/0701066] [INSPIRE].
R. Bhattacharyya, S. Collins and R. de Mello Koch, Exact Multi-Matrix Correlators, JHEP 03 (2008) 044 [arXiv:0801.2061] [INSPIRE].
Y. Kimura and S. Ramgoolam, Branes, anti-branes and brauer algebras in gauge-gravity duality, JHEP 11 (2007) 078 [arXiv:0709.2158] [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, Enhanced symmetries of gauge theory and resolving the spectrum of local operators, Phys. Rev. D 78 (2008) 126003 [arXiv:0807.3696] [INSPIRE].
R. Bhattacharyya, R. de Mello Koch and M. Stephanou, Exact Multi-Restricted Schur Polynomial Correlators, JHEP 06 (2008) 101 [arXiv:0805.3025] [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, M. Dessein, D. Giataganas and C. Mathwin, Giant Graviton Oscillators, JHEP 10 (2011) 009 [arXiv:1108.2761] [INSPIRE].
R. de Mello Koch, J. Smolic and M. Smolic, Giant Gravitons — with Strings Attached (II), JHEP 09 (2007) 049 [hep-th/0701067] [INSPIRE].
T.W. Brown, Permutations and the Loop, JHEP 06 (2008) 008 [arXiv:0801.2094] [INSPIRE].
R. de Mello Koch, P. Diaz and N. Nokwara, Restricted Schur Polynomials for Fermions and integrability in the SU(2|3) sector, JHEP 03 (2013) 173 [arXiv:1212.5935] [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 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].
R. de Mello Koch, N.H. Tahiridimbisoa and C. Mathwin, Anomalous Dimensions of Heavy Operators from Magnon Energies, JHEP 03 (2016) 156 [arXiv:1506.05224] [INSPIRE].
W. Carlson, R. de Mello Koch and H. Lin, Nonplanar Integrability, JHEP 03 (2011) 105 [arXiv:1101.5404] [INSPIRE].
R. de Mello Koch, N. Ives and M. Stephanou, On subgroup adapted bases for representations of the symmetric group, J. Phys. A 45 (2012) 135204 [arXiv:1112.4316] [INSPIRE].
R. de Mello Koch and S. Ramgoolam, Strings from Feynman Graph counting: without large N , Phys. Rev. D 85 (2012) 026007 [arXiv:1110.4858] [INSPIRE].
D. Sadri and M.M. Sheikh-Jabbari, Giant hedgehogs: Spikes on giant gravitons, Nucl. Phys. B 687 (2004) 161 [hep-th/0312155] [INSPIRE].
S. de Carvalho, R. de Mello Koch and M. Kim, Central Charges for the Double Coset, JHEP 05 (2020) 007 [arXiv:2001.10181] [INSPIRE].
N. Beisert, The SU(2|3) dynamic spin chain, Nucl. Phys. B 682 (2004) 487 [hep-th/0310252] [INSPIRE].
B. Eden, C. Jarczak and E. Sokatchev, A Three-loop test of the dilatation operator in N = 4 SYM, Nucl. Phys. B 712 (2005) 157 [hep-th/0409009] [INSPIRE].
R. de Mello Koch, S. Graham and W. Mabanga, Subleading corrections to the Double Coset Ansatz preserve integrability, JHEP 02 (2014) 079 [arXiv:1312.6230] [INSPIRE].
S. de Carvalho, R. de Mello Koch and A. Larweh Mahu, Anomalous dimensions from boson lattice models, Phys. Rev. D 97 (2018) 126004 [arXiv:1801.02822] [INSPIRE].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
R. de Mello Koch, G. Mashile and N. Park, Emergent Threebrane Lattices, Phys. Rev. D 81 (2010) 106009 [arXiv:1004.1108] [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].
R. de Mello Koch, P. Diaz and H. Soltanpanahi, Non-planar Anomalous Dimensions in the sl(2) Sector, Phys. Lett. B 713 (2012) 509 [arXiv:1111.6385] [INSPIRE].
J.M. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
A. Kitaev, A simple model of quantum holography. Part 2, talk given at the Entanglement in Strongly-Correlated Quantum Matter, Santa Barbara, California, U.S.A., 6 April–2 July 2015 and online at http://online.kitp.ucsb.edu/online/entangled15/kitaev2.
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
J.M. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
N. Beisert, The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 945 [hep-th/0511082] [INSPIRE].
N. Beisert, The Analytic Bethe Ansatz for a Chain with Centrally Extended su(2|2) Symmetry, J. Stat. Mech. 0701 (2007) P01017 [nlin/0610017] [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].
R. de Mello Koch, C. Mathwin and H.J.R. Van Zyl, LLM Magnons, JHEP 03 (2016) 110 [arXiv:1601.06914] [INSPIRE].
R. de Mello Koch, M. Kim and H.J.R. Van Zyl, Integrable Subsectors from Holography, JHEP 05 (2018) 198 [arXiv:1802.01367] [INSPIRE].
M. Kim and H.J.R. Van Zyl, Semiclassical SL(2) strings on LLM backgrounds, Phys. Lett. B 784 (2018) 62 [arXiv:1805.12460] [INSPIRE].
R. de Mello Koch, J.-H. Huang and L. Tribelhorn, Exciting LLM Geometries, JHEP 07 (2018) 146 [arXiv:1806.06586] [INSPIRE].
R. Suzuki, Three-point functions in \( \mathcal{N} \) = 4 SYM at finite Nc and background independence, JHEP 05 (2020) 118 [arXiv:2002.07216] [INSPIRE].
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de Mello Koch, R., Huang, JH., Kim, M. et al. Emergent Yang-Mills theory. J. High Energ. Phys. 2020, 100 (2020). https://doi.org/10.1007/JHEP10(2020)100
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DOI: https://doi.org/10.1007/JHEP10(2020)100