×

Central charges for the double coset. (English) Zbl 1437.83152

Summary: The state space of excited giant graviton brane systems is given by the Gauss graph operators. After restricting to the \( su(2|3) \) sector of the theory, we consider this state space. Our main result is the decomposition of this state space into irreducible representations of the \( su (2|2) \ltimes \mathbb{R}\) global symmetry. Excitations of the giant graviton branes are charged under a central extension of the global symmetry. The central extension generates gauge transformations so that the action of the central extension vanishes on physical states. Indeed, we explicitly demonstrate that the central charge is set to zero by the Gauss Law of the brane world volume gauge theory.

MSC:

83E50 Supergravity
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Maldacena, JM, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys., 38, 1113 (1999) · Zbl 0969.81047 · doi:10.1023/A:1026654312961
[2] Gubser, SS; Klebanov, IR; Polyakov, AM, Gauge theory correlators from noncritical string theory, Phys. Lett., B 428, 105 (1998) · Zbl 1355.81126 · doi:10.1016/S0370-2693(98)00377-3
[3] Witten, E., Anti-de Sitter space and holography, Adv. Theor. Math. Phys., 2, 253 (1998) · Zbl 0914.53048 · doi:10.4310/ATMP.1998.v2.n2.a2
[4] Minahan, JA; Zarembo, K., The Bethe ansatz for N = 4 super Yang-Mills, JHEP, 03, 013 (2003) · doi:10.1088/1126-6708/2003/03/013
[5] Beisert, N., Review of AdS/CFT integrability: an overview, Lett. Math. Phys., 99, 3 (2012) · Zbl 1268.81126 · doi:10.1007/s11005-011-0529-2
[6] Beisert, N., The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys., 12, 945 (2008) · Zbl 1146.81047 · doi:10.4310/ATMP.2008.v12.n5.a1
[7] N. Beisert, The analytic Bethe ansatz for a chain with centrally extended su(2|2) symmetry, J. Stat. Mech.0701 (2007) P01017 [nlin/0610017]. · Zbl 1456.82226
[8] Balasubramanian, V.; Berkooz, M.; Naqvi, A.; Strassler, MJ, Giant gravitons in conformal field theory, JHEP, 04, 034 (2002) · doi:10.1088/1126-6708/2002/04/034
[9] Corley, S.; Jevicki, A.; Ramgoolam, S., Exact correlators of giant gravitons from dual N = 4 SYM theory, Adv. Theor. Math. Phys., 5, 809 (2002) · Zbl 1136.81406 · doi:10.4310/ATMP.2001.v5.n4.a6
[10] Aharony, O.; Antebi, YE; Berkooz, M.; Fishman, R., ‘Holey sheets’: Pfaffians and subdeterminants as D-brane operators in large N gauge theories, JHEP, 12, 069 (2002) · doi:10.1088/1126-6708/2002/12/069
[11] Berenstein, D., A toy model for the AdS/CFT correspondence, JHEP, 07, 018 (2004) · doi:10.1088/1126-6708/2004/07/018
[12] Balasubramanian, V.; Berenstein, D.; Feng, B.; Huang, M-X, D-branes in Yang-Mills theory and emergent gauge symmetry, JHEP, 03, 006 (2005)
[13] de Mello Koch, R.; Smolic, J.; Smolic, M., Giant gravitons — with strings attached (I), JHEP, 06, 074 (2007) · doi:10.1088/1126-6708/2007/06/074
[14] de Mello Koch, R.; Smolic, J.; Smolic, M., Giant gravitons — with strings attached (II), JHEP, 09, 049 (2007) · doi:10.1088/1126-6708/2007/09/049
[15] Bekker, D.; de Mello Koch, R.; Stephanou, M., Giant gravitons — with strings attached (III), JHEP, 02, 029 (2008) · doi:10.1088/1126-6708/2008/02/029
[16] Kimura, Y.; Ramgoolam, S., Branes, anti-branes and Brauer algebras in gauge-gravity duality, JHEP, 11, 078 (2007) · Zbl 1245.81189 · doi:10.1088/1126-6708/2007/11/078
[17] Brown, TW; Heslop, PJ; Ramgoolam, S., Diagonal multi-matrix correlators and BPS operators in N = 4 SYM, JHEP, 02, 030 (2008) · doi:10.1088/1126-6708/2008/02/030
[18] Bhattacharyya, R.; Collins, S.; de Mello Koch, R., Exact multi-matrix correlators, JHEP, 03, 044 (2008) · doi:10.1088/1126-6708/2008/03/044
[19] Brown, TW; Heslop, PJ; Ramgoolam, S., Diagonal free field matrix correlators, global symmetries and giant gravitons, JHEP, 04, 089 (2009) · doi:10.1088/1126-6708/2009/04/089
[20] Bhattacharyya, R.; de Mello Koch, R.; Stephanou, M., Exact multi-restricted Schur polynomial correlators, JHEP, 06, 101 (2008) · doi:10.1088/1126-6708/2008/06/101
[21] Kimura, Y.; Ramgoolam, S., Enhanced symmetries of gauge theory and resolving the spectrum of local operators, Phys. Rev., D 78, 126003 (2008)
[22] de Mello Koch, R.; Dessein, M.; Giataganas, D.; Mathwin, C., Giant graviton oscillators, JHEP, 10, 009 (2011) · Zbl 1303.81119 · doi:10.1007/JHEP10(2011)009
[23] de Mello Koch, R.; Kemp, G.; Smith, S., From large N nonplanar anomalous dimensions to open spring theory, Phys. Lett., B 711, 398 (2012) · doi:10.1016/j.physletb.2012.04.018
[24] de Mello Koch, R.; Ramgoolam, S., A double coset ansatz for integrability in AdS/CFT, JHEP, 06, 083 (2012) · Zbl 1397.81288 · doi:10.1007/JHEP06(2012)083
[25] de Mello Koch, R.; Graham, S.; Mabanga, W., Subleading corrections to the double coset ansatz preserve integrability, JHEP, 02, 079 (2014) · Zbl 1333.81147 · doi:10.1007/JHEP02(2014)079
[26] A. Mohamed Adam Ali, R. de Mello Koch, N.H. Tahiridimbisoa and A. Larweh Mahu, Interacting double coset magnons, Phys. Rev.D 93 (2016) 065057 [arXiv:1512.05019] [INSPIRE].
[27] de Carvalho, S.; de Mello Koch, R.; Larweh Mahu, A., Anomalous dimensions from boson lattice models, Phys. Rev., D 97, 126004 (2018)
[28] de Mello Koch, R.; Graham, S.; Messamah, I., Higher loop nonplanar anomalous dimensions from symmetry, JHEP, 02, 125 (2014) · doi:10.1007/JHEP02(2014)125
[29] Berenstein, D., On the central charge extension of the N = 4 SYM spin chain, JHEP, 05, 129 (2015) · doi:10.1007/JHEP05(2015)129
[30] Berenstein, D., Giant gravitons: a collective coordinate approach, Phys. Rev., D 87, 126009 (2013)
[31] Berenstein, D.; Dzienkowski, E., Open spin chains for giant gravitons and relativity, JHEP, 08, 047 (2013) · Zbl 1470.83054 · doi:10.1007/JHEP08(2013)047
[32] Berenstein, D.; Dzienkowski, E., Giant gravitons and the emergence of geometric limits in β-deformations of N = 4 SYM, JHEP, 01, 126 (2015) · doi:10.1007/JHEP01(2015)126
[33] Beisert, N., The SU(2|3) dynamic spin chain, Nucl. Phys., B 682, 487 (2004) · Zbl 1036.82513 · doi:10.1016/j.nuclphysb.2003.12.032
[34] de Mello Koch, R.; Diaz, P.; Nokwara, N., Restricted Schur polynomials for fermions and integrability in the SU(2|3) sector, JHEP, 03, 173 (2013) · Zbl 1342.81299 · doi:10.1007/JHEP03(2013)173
[35] Berenstein, D.; de Mello Koch, R., Gauged fermionic matrix quantum mechanics, JHEP, 03, 185 (2019) · Zbl 1414.81192 · doi:10.1007/JHEP03(2019)185
[36] Fulton, W.; Harris, J., Representation theory: a first course (2004), New York, NY, U.S.A.: Springer, New York, NY, U.S.A.
[37] De Comarmond, V.; de Mello Koch, R.; Jefferies, K., Surprisingly simple spectra, JHEP, 02, 006 (2011) · Zbl 1294.81098
[38] Carlson, W.; de Mello Koch, R.; Lin, H., Nonplanar integrability, JHEP, 03, 105 (2011) · Zbl 1301.81112 · doi:10.1007/JHEP03(2011)105
[39] Stefanski, B. Jr; Tseytlin, AA, Super spin chain coherent state actions and AdS_5 × S^5superstring, Nucl. Phys., B 718, 83 (2005) · Zbl 1207.81138 · doi:10.1016/j.nuclphysb.2005.04.026
[40] Lin, H., Relation between large dimension operators and oscillator algebra of Young diagrams, Int. J. Geom. Meth. Mod. Phys., 12, 1550047 (2015) · Zbl 1316.81072 · doi:10.1142/S0219887815500474
[41] Berenstein, DE; Maldacena, JM; Nastase, HS, Strings in flat space and pp waves from N = 4 super Yang-Mills, JHEP, 04, 013 (2002) · doi:10.1088/1126-6708/2002/04/013
[42] Bornman, N.; de Mello Koch, R.; Tribelhorn, L., Rotating restricted Schur polynomials, Int. J. Mod. Phys., A 32, 1750150 (2017) · Zbl 1378.81068 · doi:10.1142/S0217751X17501500
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.