Infinite symmetry on the boundary of \(\mathrm{SL}(3)/\mathrm{SO}(3)\). (English) Zbl 1274.81121
Summary: Asymptotic symmetries of the five-dimensional noncompact symmetric space \(\mathrm{SL}(3,\mathbb R)/\mathrm{SO}(3,\mathbb R)\) are found to form an infinite-dimensional Lie algebra, analogously to the asymptotic symmetries of anti-de Sitter/hyperbolic spaces in two and three dimensions. Possible generalizations of the AdS/CFT correspondence and gauge/gravity dualities to such a space is discussed.{
©2012 American Institute of Physics}
©2012 American Institute of Physics}
MSC:
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
| 17B81 | Applications of Lie (super)algebras to physics, etc. |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 83E15 | Kaluza-Klein and other higher-dimensional theories |
| 53C35 | Differential geometry of symmetric spaces |
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
References:
| [1] | Penrose R., Spinors and Spacetime, vol. 2: Spinor and Twistor Methods in Space-Time Geometry (1986) · doi:10.1017/CBO9780511524486 |
| [2] | DOI: 10.1016/S0920-5632(03)02410-1 · doi:10.1016/S0920-5632(03)02410-1 |
| [3] | DOI: 10.1007/BF01211590 · Zbl 0584.53039 · doi:10.1007/BF01211590 |
| [4] | DOI: 10.1088/1126-6708/1998/07/006 · Zbl 0958.81081 · doi:10.1088/1126-6708/1998/07/006 |
| [5] | DOI: 10.1088/0264-9381/12/12/012 · Zbl 0836.53052 · doi:10.1088/0264-9381/12/12/012 |
| [6] | DOI: 10.1103/PhysRevD.48.1506 · doi:10.1103/PhysRevD.48.1506 |
| [7] | DOI: 10.1016/0370-2693(86)90140-1 · doi:10.1016/0370-2693(86)90140-1 |
| [8] | DOI: 10.1007/BF01217730 · Zbl 0667.57005 · doi:10.1007/BF01217730 |
| [9] | DOI: 10.1088/1126-6708/1998/02/009 · Zbl 0955.83010 · doi:10.1088/1126-6708/1998/02/009 |
| [10] | DOI: 10.1007/JHEP02(2011)004 · Zbl 1294.81105 · doi:10.1007/JHEP02(2011)004 |
| [11] | DOI: 10.1007/JHEP12(2010)007 · Zbl 1294.81137 · doi:10.1007/JHEP12(2010)007 |
| [12] | ’t Hooft G., Proceedings of the International School of Subnuclear Physics 37 pp 72– (2001) |
| [13] | DOI: 10.1063/1.531249 · Zbl 0850.00013 · doi:10.1063/1.531249 |
| [14] | DOI: 10.1007/JHEP06(2011)031 · Zbl 1298.81181 · doi:10.1007/JHEP06(2011)031 |
| [15] | Helgason S., Differential geometry, Lie Groups, and Symmetric Spaces (1981) · Zbl 0451.53038 |
| [16] | DOI: 10.1017/CBO9780511791390 · doi:10.1017/CBO9780511791390 |
| [17] | DOI: 10.1017/CBO9780511755590 · doi:10.1017/CBO9780511755590 |
| [18] | Ballmann W., Manifolds of nonpositive curvature (1985) · Zbl 0591.53001 · doi:10.1007/978-1-4684-9159-3 |
| [19] | Hermann R., Mathematical Physics Monograph Series, in: Lie groups for physicists (1966) |
| [20] | DOI: 10.1007/JHEP11(2010)007 · Zbl 1294.81240 · doi:10.1007/JHEP11(2010)007 |
| [21] | DOI: 10.1103/PhysRevD.48.1506 · doi:10.1103/PhysRevD.48.1506 |
| [22] | DOI: 10.1007/978-1-4612-2110-4 · doi:10.1007/978-1-4612-2110-4 |
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.
