\(\mathcal{N}=5\) three-algebras and 5-graded Lie superalgebras. (English) Zbl 1272.81175
Summary: We discuss a generalization of \(\mathcal{N}=6\) three-algebras to \(\mathcal{N}=5\) three-algebras in connection to anti-Lie triple systems and basic Lie superalgebras of type II. We then show that the structure constants defined in anti-Lie triple systems agree with those of \(\mathcal{N}=5\) superconformal theories in three dimensions. {
©2011 American Institute of Physics}
©2011 American Institute of Physics}
MSC:
81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
81T60 | Supersymmetric field theories in quantum mechanics |
17A70 | Superalgebras |
17B70 | Graded Lie (super)algebras |
17B25 | Exceptional (super)algebras |
18C15 | Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads |
Keywords:
anti-Lie triple systemReferences:
[1] | DOI: 10.1103/PhysRevD.77.065008 · doi:10.1103/PhysRevD.77.065008 |
[2] | DOI: 10.1016/j.nuclphysb.2008.11.014 · Zbl 1194.81205 · doi:10.1016/j.nuclphysb.2008.11.014 |
[3] | DOI: 10.1088/1126-6708/2008/10/091 · Zbl 1245.81130 · doi:10.1088/1126-6708/2008/10/091 |
[4] | DOI: 10.1103/PhysRevD.79.025002 · Zbl 1222.81264 · doi:10.1103/PhysRevD.79.025002 |
[5] | DOI: 10.1088/1126-6708/2008/09/002 · Zbl 1245.81094 · doi:10.1088/1126-6708/2008/09/002 |
[6] | DOI: 10.1088/1126-6708/2008/11/043 · doi:10.1088/1126-6708/2008/11/043 |
[7] | DOI: 10.1088/1126-6708/2008/09/101 · Zbl 1245.81081 · doi:10.1088/1126-6708/2008/09/101 |
[8] | DOI: 10.1007/JHEP06(2010)097 · Zbl 1290.81065 · doi:10.1007/JHEP06(2010)097 |
[9] | DOI: 10.1103/PhysRevD.82.106012 · doi:10.1103/PhysRevD.82.106012 |
[10] | DOI: 10.1088/1751-8113/43/1/015205 · Zbl 1180.81116 · doi:10.1088/1751-8113/43/1/015205 |
[11] | DOI: 10.1088/0264-9381/26/7/075007 · Zbl 1161.83443 · doi:10.1088/0264-9381/26/7/075007 |
[12] | DOI: 10.1007/s00220-009-0760-1 · Zbl 1259.81081 · doi:10.1007/s00220-009-0760-1 |
[13] | DOI: 10.1088/1751-8113/42/44/445206 · Zbl 1176.81123 · doi:10.1088/1751-8113/42/44/445206 |
[14] | DOI: 10.1088/1751-8113/42/48/485204 · Zbl 1179.81144 · doi:10.1088/1751-8113/42/48/485204 |
[15] | DOI: 10.1007/JHEP08(2010)077 · Zbl 1290.81139 · doi:10.1007/JHEP08(2010)077 |
[16] | DOI: 10.1103/PhysRevD.83.025003 · doi:10.1103/PhysRevD.83.025003 |
[17] | DOI: 10.1007/BF01609166 · Zbl 0359.17009 · doi:10.1007/BF01609166 |
[18] | Frappat L., Dictionary on Lie Algebras and Superalgebras (2000) · Zbl 0965.17001 |
[19] | DOI: 10.1007/JHEP05(2011)088 · Zbl 1296.81066 · doi:10.1007/JHEP05(2011)088 |
[20] | DOI: 10.1063/1.523109 · Zbl 0335.17015 · doi:10.1063/1.523109 |
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.