Abstract
We study spin chains with boundaries that are dual to open strings suspended between systems of giant gravitons and dual giant gravitons. Motivated by a geometrical interpretation of the central charges of su(2|2), we propose a simple and minimal all loop expression that interpolates between the anomalous dimensions computed in the gauge theory and energies computed in the dual string theory. The discussion makes use of a description in terms of magnons, generalizing results for a single maximal giant graviton. The symmetries of the problem determine the structure of the magnon boundary reflection/scattering matrix up to a phase. We compute a reflection/scattering matrix element at weak coupling and verify that it is consistent with the answer determined by symmetry. We find the reflection/scattering matrix does not satisfy the boundary Yang-Baxter equation so that the boundary condition on the open spin chain spoils integrability. We also explain the interpretation of the double coset ansatz in the magnon language.
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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].
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [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] [INSPIRE].
D.M. Hofman and J.M. Maldacena, Reflecting magnons, JHEP 11 (2007) 063 [arXiv:0708.2272] [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].
D. Berenstein, A toy model for the AdS/CFT correspondence, JHEP 07 (2004) 018 [hep-th/0403110] [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].
V. Balasubramanian, M. Berkooz, A. Naqvi and M.J. Strassler, Giant gravitons in conformal field theory, JHEP 04 (2002) 034 [hep-th/0107119] [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].
S. Corley and S. Ramgoolam, Finite factorization equations and sum rules for BPS correlators in N = 4 SYM theory, Nucl. Phys. B 641 (2002) 131 [hep-th/0205221] [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 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].
Y. Kimura, Non-holomorphic multi-matrix gauge invariant operators based on Brauer algebra, JHEP 12 (2009) 044 [arXiv:0910.2170] [INSPIRE].
Y. Kimura, S. Ramgoolam and D. Turton, Free particles from Brauer algebras in complex matrix models, JHEP 05 (2010) 052 [arXiv:0911.4408] [INSPIRE].
Y. Kimura, Quarter BPS classified by Brauer algebra, JHEP 05 (2010) 103 [arXiv:1002.2424] [INSPIRE].
Y. Kimura and H. Lin, Young diagrams, Brauer algebras and bubbling geometries, JHEP 01 (2012) 121 [arXiv:1109.2585] [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].
Y. Kimura, Non-planar operator mixing by Brauer representations, Nucl. Phys. B 875 (2013) 790 [arXiv:1302.6404] [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. 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].
R. Bhattacharyya, S. Collins and R. de Mello Koch, Exact Multi-Matrix Correlators, JHEP 03 (2008) 044 [arXiv:0801.2061] [INSPIRE].
R. Bhattacharyya, R. de Mello Koch and M. Stephanou, Exact Multi-Restricted Schur Polynomial Correlators, JHEP 06 (2008) 101 [arXiv:0805.3025] [INSPIRE].
R. de Mello Koch, G. Mashile and N. Park, Emergent Threebrane Lattices, Phys. Rev. D 81 (2010) 106009 [arXiv:1004.1108] [INSPIRE].
V. De Comarmond, R. de Mello Koch and K. Jefferies, Surprisingly Simple Spectra, JHEP 02 (2011) 006 [arXiv:1012.3884] [INSPIRE].
W. Carlson, R. de Mello Koch and H. Lin, Nonplanar Integrability, JHEP 03 (2011) 105 [arXiv:1101.5404] [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 and S. Ramgoolam, A double coset ansatz for integrability in AdS/CFT, JHEP 06 (2012) 083 [arXiv:1204.2153] [INSPIRE].
R. de Mello Koch, G. Kemp and S. Smith, From Large-N Nonplanar Anomalous Dimensions to Open Spring Theory, Phys. Lett. B 711 (2012) 398 [arXiv:1111.1058] [INSPIRE].
P. Caputa, R. de Mello Koch and P. Diaz, A basis for large operators in N = 4 SYM with orthogonal gauge group, JHEP 03 (2013) 041 [arXiv:1301.1560] [INSPIRE].
P. Caputa, R. de Mello Koch and P. Diaz, Operators, Correlators and Free Fermions for SO(N ) and Sp(N ), JHEP 06 (2013) 018 [arXiv:1303.7252] [INSPIRE].
P. Diaz, Orthogonal Schurs for Classical Gauge Groups, JHEP 10 (2013) 228 [arXiv:1309.1180] [INSPIRE].
G. Kemp, SO(N ) restricted Schur polynomials, J. Math. Phys. 56 (2015) 022302 [arXiv:1405.7017] [INSPIRE].
G. Kemp, Restricted Schurs and correlators for SO(N ) and Sp(N ), JHEP 08 (2014) 137 [arXiv:1406.3854] [INSPIRE].
P. Diaz, Novel charges in CFT‘s, JHEP 09 (2014) 031 [arXiv:1406.7671] [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].
Y. Kimura and R. Suzuki, Negative anomalous dimensions in \( \mathcal{N} = 4 \) SYM, Nucl. Phys. B 900 (2015) 603 [arXiv:1503.06210] [INSPIRE].
V. Balasubramanian, M.-x. Huang, T.S. Levi and A. Naqvi, Open strings from N = 4 super Yang-Mills, JHEP 08 (2002) 037 [hep-th/0204196] [INSPIRE].
S.R. Das, A. Jevicki and S.D. Mathur, Vibration modes of giant gravitons, Phys. Rev. D 63 (2001) 024013 [hep-th/0009019] [INSPIRE].
O. Aharony, Y.E. Antebi, M. Berkooz and R. Fishman, ’Holey sheets’: Pfaffians and subdeterminants as D-brane operators in large-N gauge theories, JHEP 12 (2002) 069 [hep-th/0211152] [INSPIRE].
D. Berenstein, Shape and holography: Studies of dual operators to giant gravitons, Nucl. Phys. B 675 (2003) 179 [hep-th/0306090] [INSPIRE].
D. Berenstein, D.H. Correa and S.E. Vazquez, A study of open strings ending on giant gravitons, spin chains and integrability, JHEP 09 (2006) 065 [hep-th/0604123] [INSPIRE].
D. Berenstein and S.E. Vazquez, Integrable open spin chains from giant gravitons, JHEP 06 (2005) 059 [hep-th/0501078] [INSPIRE].
D. Berenstein, D.H. Correa and S.E. Vazquez, Quantizing open spin chains with variable length: An example from giant gravitons, Phys. Rev. Lett. 95 (2005) 191601 [hep-th/0502172] [INSPIRE].
D. Garner, S. Ramgoolam and C. Wen, Thresholds of large-N factorization in CFT 4 : exploring bulk spacetime in AdS 5, JHEP 11 (2014) 076 [arXiv:1403.5281] [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, 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].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [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].
A. Hashimoto, S. Hirano and N. Itzhaki, Large branes in AdS and their field theory dual, JHEP 08 (2000) 051 [hep-th/0008016] [INSPIRE].
M.T. Grisaru, R.C. Myers and O. Tafjord, SUSY and goliath, JHEP 08 (2000) 040 [hep-th/0008015] [INSPIRE].
R.A. Janik, The AdS 5 × S 5 superstring worldsheet S-matrix and crossing symmetry, Phys. Rev. D 73 (2006) 086006 [hep-th/0603038] [INSPIRE].
D.H. Correa and C.A.S. Young, Asymptotic Bethe equations for open boundaries in planar AdS/CFT, J. Phys. A 43 (2010) 145401 [arXiv:0912.0627] [INSPIRE].
H. Lin, Relation between large dimension operators and oscillator algebra of Young diagrams, Int. J. Geom. Meth. Mod. Phys. 12 (2015) 1550047 [arXiv:1407.7815] [INSPIRE].
F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [INSPIRE].
M. Staudacher, The factorized S-matrix of CFT/AdS, JHEP 05 (2005) 054 [hep-th/0412188] [INSPIRE].
L. Freyhult, C. Kristjansen and T. Mansson, Integrable spin chains with U(1)3 symmetry and generalized Lunin-Maldacena backgrounds, JHEP 12 (2005) 008 [hep-th/0510221] [INSPIRE].
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de Mello Koch, R., Tahiridimbisoa, N.H. & Mathwin, C. Anomalous dimensions of heavy operators from magnon energies. J. High Energ. Phys. 2016, 156 (2016). https://doi.org/10.1007/JHEP03(2016)156
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DOI: https://doi.org/10.1007/JHEP03(2016)156