544:, with the associated symmetry known as supersymmetry. The Haag–Łopuszański–Sohnius theorem is the generalization of the Coleman–Mandula theorem to Lie superalgebras, with it stating that supersymmetry is the only new spacetime dependent symmetry that is allowed. For a theory with massless particles, the theorem is again evaded by conformal symmetry which can be present in addition to supersymmetry giving a
556:
In a one or two dimensional theory the only possible scattering is forwards and backwards scattering so analyticity of the scattering angles is no longer possible and the theorem no longer holds. Spacetime dependent internal symmetries are then possible, such as in the massive
327:
could belong to the same multiplet. Such a symmetry could then account for the mass splitting found in mesons and baryons. It was only later understood that this is instead a consequence of the differing up-, down-, and strange-quark masses which leads to a breakdown of the
362:
These two motivations led to a series of no-go theorems to show that spacetime symmetries and internal symmetries could not be combined in any but a trivial way. The first notable theorem was proved by
William McGlinn in 1964, with a subsequent generalization by
379:, rather than from any attempts to overcome the no-go theorem. Similarly, the Haag–Łopuszański–Sohnius theorem, a supersymmetric generalization of the Coleman–Mandula theorem, was proved in 1975 after the study of supersymmetry was already underway.
59:
who proved it in 1967 as the culmination of a series of increasingly generalized no-go theorems investigating how internal symmetries can be combined with spacetime symmetries. The supersymmetric generalization is known as the
474:
the amplitudes, making them nonzero only at discrete scattering angles. Since this conflicts with the assumption of the analyticity of the scattering angles, such additional spacetime dependent symmetries are ruled out.
370:
Little notice was given to this theorem in subsequent years. As a result, the theorem played no role in the early development of supersymmetry, which instead emerged in the early 1970s from the study of
470:. The argument is that Poincaré symmetry acts as a very strong constraint on elastic scattering, leaving only the scattering angle unknown. Any additional spacetime dependent symmetry would
357:
314:
256:
225:
182:
151:
104:
277:
decuplets into a 56-dimensional multiplet. While this was reasonably successful in describing various aspects of the hadron spectrum, from the perspective of
1155:
Fotopoulos, A.; Tsulaia, M. (2010). "On the
Tensionless Limit of String theory, Off - Shell Higher Spin Interaction Vertices and BCFW Recursion Relations".
1447:
1295:
1594:
1543:
61:
1579:
1569:
1548:
455:
of the
Poincaré group and an internal symmetry group. The last technical assumption is unnecessary if the theory is described by a
1882:
1589:
39:
can only combine in a trivial way. This means that the charges associated with internal symmetries must always transform as
1599:
1268:
1288:
1053:
1025:
948:
842:
810:
1715:
1604:
1328:
968:
505:
1642:
1637:
1574:
492:, with these allowing for conformal symmetry as an additional spacetime dependent symmetry. In particular, the
367:
in 1965. These efforts culminated with the most general theorem by Sidney
Coleman and Jeffrey Mandula in 1967.
1872:
1281:
617:
497:
323:
At the time it was also an open question whether there existed a symmetry for which particles of different
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125:
78:
1517:
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symmetries which avoid the theorem because the corresponding algebra is no longer a Lie algebra.
436:
107:
1877:
1627:
1477:
1381:
629:
605:
545:
537:
281:
this success is merely a consequence of the flavour and spin independence of the force between
278:
1263:
708:"On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei"
1657:
1652:
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1502:
1406:
1386:
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1082:
984:
913:
871:
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719:
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634:
493:
456:
451:
The
Coleman–Mandula theorem states that the symmetry group of this theory is necessarily a
421:
372:
317:
32:
8:
1662:
1647:
1632:
1401:
609:
562:
500:, which consists of the Poincaré algebra together with the commutation relations for the
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111:
20:
1239:
1231:
1178:
1125:
1086:
988:
917:
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771:
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since these do not act on the S-matrix level and thus do not commute with the S-matrix.
1771:
1343:
1338:
1243:
1217:
1190:
1164:
1137:
783:
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of one-particle states, evade the theorem. Such an evasion is found more generally for
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263:
44:
36:
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1094:
1049:
1041:
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613:
489:
429:
1247:
787:
404:
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1371:
1358:
1235:
1182:
1129:
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992:
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685:
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For other spacetime symmetries besides the
Poincaré group, such as theories with a
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56:
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119:
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40:
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symmetries whose charges do not act on multiparticle states as if they were a
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1846:
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1411:
1348:
1318:
1304:
703:
689:
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467:
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28:
16:
No-go theorem pertaining the triviality of space-time and internal symmetries
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1700:
1427:
964:
860:"Problem of Combining Interaction Symmetries and Relativistic Invariance"
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529:
517:
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The
Coleman–Mandula theorem assumes that the only symmetry algebras are
1745:
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Below any mass, there are only a finite number of particle types,
1273:
1467:
1457:
566:
533:
414:
285:. There were many attempts to generalize this non-relativistic
274:
115:
1680:
413:
Any two-particle state undergoes some reaction at almost all
282:
266:
1208:
Fabrizio, N.; Percacci, R. (2008). "Graviweak
Unification".
973:"All possible generators of supersymmetries of the S-matrix"
520:, but the theorem can be generalized by instead considering
459:
and is only needed to apply the theorem in a wider context.
1110:"Quantum group symmetries and non-local currents in 2D QFT"
1020:. Vol. 3. Cambridge University Press. pp. 12–22.
612:, the theorem no longer applies. It also does not hold for
324:
188:
and spin, an idea similar to that previously considered in
432:
of the scattering angle at almost all energies and angles,
466:
argument for why the theorem should hold was provided by
963:
835:
334:
291:
233:
202:
159:
128:
81:
668:(1967). "All Possible Symmetries of the S Matrix".
43:. Some notable exceptions to the no-go theorem are
1071:"Conserved currents in the massive thirring model"
896:
351:
308:
250:
219:
176:
145:
98:
1154:
837:. World Scientific Publishing. pp. 184–185.
1864:
1207:
1068:
1269:Sascha Leonhardt on the Coleman–Mandula theorem
1107:
941:Conceptual Foundations of Quantum Field Theory
660:
387:Consider a theory that can be described by an
1289:
1046:The Unity of the Fundamental Interactions: 19
391:and that satisfies the following conditions
1069:Berg, B.; Karowski, M.; Thun, H.J. (1976).
1018:The Quantum Theory of Fields: Supersymmetry
1008:
1006:
943:. Cambridge University Press. p. 282.
825:
122:. This led to efforts to expand the global
1296:
1282:
902:"Lorentz Invariance and Internal Symmetry"
748:(2009). "From symmetry to supersymmetry".
488:The theorem does not apply to a theory of
1221:
1168:
761:
616:, since these are not Lie groups, or for
1040:
1012:
1003:
269:of different spin into a 35-dimensional
1264:Coleman–Mandula theorem on Scholarpedia
857:
110:was shown to successfully describe the
1865:
1114:Communications in Mathematical Physics
800:
702:
435:A technical assumption that the group
1277:
803:Concise Encyclopedia of Supersymmetry
561:which can admit an infinite tower of
483:
744:
656:
654:
595:
106:flavor symmetry associated with the
938:
540:. This extension gives rise to the
524:. Doing this allows for additional
13:
1257:
14:
1899:
1303:
1108:Bernard, D.; LeClair, A. (1991).
651:
575:
551:
506:special conformal transformations
1329:Supersymmetric quantum mechanics
511:
227:symmetry. This non-relativistic
62:Haag–Łopuszański–Sohnius theorem
1201:
1148:
1101:
1062:
1034:
750:The European Physical Journal C
618:spontaneously broken symmetries
1048:. Springer. pp. 305–315.
957:
932:
890:
851:
819:
805:. Springer. pp. 265–266.
794:
780:10.1140/epjc/s10052-008-0837-6
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696:
478:
352:{\displaystyle {\text{SU}}(3)}
346:
340:
309:{\displaystyle {\text{SU}}(6)}
303:
297:
251:{\displaystyle {\text{SU}}(6)}
245:
239:
220:{\displaystyle {\text{SU}}(4)}
214:
208:
177:{\displaystyle {\text{SU}}(6)}
171:
165:
146:{\displaystyle {\text{SU}}(3)}
140:
134:
99:{\displaystyle {\text{SU}}(3)}
93:
87:
1:
1883:Theorems in quantum mechanics
1240:10.1088/1751-8113/41/7/075405
375:, which are the precursor to
1095:10.1016/0370-2693(76)90203-3
997:10.1016/0550-3213(75)90279-5
7:
1324:Supersymmetric gauge theory
623:
320:one, but these all failed.
273:and it also united the two
10:
1904:
1623:Pure 4D N = 1 supergravity
884:10.1103/PhysRevLett.12.467
382:
359:internal flavor symmetry.
67:
1754:
1671:
1613:
1557:
1531:
1523:Electric–magnetic duality
1420:
1357:
1311:
926:10.1103/PhysRev.139.B1052
1544:Haag–Łopuszański–Sohnius
1518:Little hierarchy problem
939:Cao, T.Y. (2004). "19".
690:10.1103/PhysRev.159.1251
645:
428:two-body scattering are
365:Lochlainn O'Raifeartaigh
72:In the early 1960s, the
1600:6D (2,0) superconformal
1187:10.1007/JHEP11(2010)086
538:Lorentz transformations
25:Coleman–Mandula theorem
1580:N = 4 super Yang–Mills
1570:N = 1 super Yang–Mills
1478:Supersymmetry breaking
1382:Superconformal algebra
1377:Super-Poincaré algebra
971:; Sohnius, M. (1975).
858:McGlinn, W.D. (1964).
732:10.1103/PhysRev.51.106
630:Extended supersymmetry
546:superconformal algebra
542:super-Poincaré algebra
353:
310:
279:quantum chromodynamics
252:
221:
178:
147:
100:
1658:Type IIB supergravity
1653:Type IIA supergravity
1628:4D N = 1 supergravity
1493:Seiberg–Witten theory
1407:Super Minkowski space
1387:Supersymmetry algebra
640:Supersymmetry algebra
496:of this group is the
373:dual resonance models
354:
311:
253:
222:
184:symmetry mixing both
179:
153:symmetry to a larger
148:
101:
1873:Quantum field theory
1443:Short supermultiplet
604:or non-relativistic
602:de Sitter background
528:generators known as
457:quantum field theory
332:
289:
231:
200:
157:
126:
79:
51:. It is named after
1663:Gauged supergravity
1648:Type I supergravity
1605:ABJM superconformal
1402:Harmonic superspace
1232:2008JPhA...41g5405N
1179:2010JHEP...11..086F
1126:1991CMaPh.142...99B
1087:1976PhLB...64..286B
989:1975NuPhB..88..257H
918:1965PhRv..139.1052O
912:(4B): B1052–B1062.
876:1964PhRvL..12..467M
801:Duplij, S. (2003).
772:2009EPJC...59..177W
724:1937PhRv...51..106W
682:1967PhRv..159.1251C
614:discrete symmetries
610:Galilean invariance
532:which transform as
403:which includes the
316:model into a fully
21:theoretical physics
1638:Higher dimensional
1633:N = 8 supergravity
1549:Nonrenormalization
1344:Super vector space
1339:Superstring theory
1134:10.1007/BF02099173
898:O'Raifeartaigh, L.
504:generator and the
490:massless particles
484:Conformal symmetry
430:analytic functions
349:
306:
248:
217:
174:
143:
96:
45:conformal symmetry
1860:
1859:
1503:Wess–Zumino gauge
1075:Physics Letters B
977:Nuclear Physics B
969:Łopuszański, J.T.
596:Other limitations
563:conserved charges
522:Lie superalgebras
498:conformal algebra
338:
295:
237:
206:
163:
132:
85:
1895:
1643:11D supergravity
1372:Lie superalgebra
1359:Supermathematics
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676:(5): 1251–1256.
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1553:
1539:Coleman–Mandula
1527:
1488:Seiberg duality
1483:Konishi anomaly
1416:
1353:
1307:
1302:
1260:
1258:Further reading
1255:
1206:
1202:
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1028:
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951:
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933:
895:
891:
870:(16): 467–469.
864:Phys. Rev. Lett
856:
852:
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820:
813:
799:
795:
743:
739:
701:
697:
659:
652:
648:
626:
598:
578:
565:of ever higher
554:
526:anticommutating
514:
486:
481:
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335:
333:
330:
329:
292:
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234:
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201:
198:
197:
196:in 1937 for an
190:nuclear physics
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155:
154:
129:
127:
124:
123:
112:hadron spectrum
82:
80:
77:
76:
70:
57:Jeffrey Mandula
41:Lorentz scalars
17:
12:
11:
5:
1901:
1891:
1890:
1888:No-go theorems
1885:
1880:
1875:
1858:
1857:
1855:
1854:
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1558:Field theories
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1453:Superpotential
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1445:
1440:
1438:Supermultiplet
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1312:General topics
1309:
1308:
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1286:
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1271:
1266:
1259:
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1254:
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1200:
1147:
1100:
1081:(3): 286–288.
1061:
1055:978-1461336570
1054:
1033:
1027:978-0521670555
1026:
1016:(2005). "24".
1002:
983:(2): 257–274.
956:
950:978-0521602723
949:
931:
889:
850:
844:978-9810245221
843:
818:
812:978-1402013386
811:
793:
756:(2): 177–183.
737:
718:(2): 106–119.
695:
649:
647:
644:
643:
642:
637:
632:
625:
622:
606:field theories
597:
594:
586:tensor product
577:
576:Quantum groups
574:
559:Thirring model
553:
552:Low dimensions
550:
513:
510:
485:
482:
480:
477:
453:direct product
449:
448:
445:momentum space
433:
418:
411:
408:
407:as a subgroup,
405:Poincaré group
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53:Sidney Coleman
15:
9:
6:
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1900:
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1878:Supersymmetry
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1673:Superpartners
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1413:
1412:Supermanifold
1410:
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1349:Supergeometry
1347:
1345:
1342:
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1332:
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1327:
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1322:
1320:
1319:Supersymmetry
1317:
1316:
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1310:
1306:
1305:Supersymmetry
1299:
1294:
1292:
1287:
1285:
1280:
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1261:
1249:
1245:
1241:
1237:
1233:
1229:
1224:
1219:
1216:(7): 075405.
1215:
1211:
1204:
1196:
1192:
1188:
1184:
1180:
1176:
1171:
1166:
1162:
1158:
1151:
1143:
1139:
1135:
1131:
1127:
1123:
1120:(1): 99–138.
1119:
1115:
1111:
1104:
1096:
1092:
1088:
1084:
1080:
1076:
1072:
1065:
1057:
1051:
1047:
1043:
1037:
1029:
1023:
1019:
1015:
1009:
1007:
998:
994:
990:
986:
982:
978:
974:
970:
966:
960:
952:
946:
942:
935:
927:
923:
919:
915:
911:
907:
903:
899:
893:
885:
881:
877:
873:
869:
865:
861:
854:
846:
840:
836:
832:
828:
822:
814:
808:
804:
797:
789:
785:
781:
777:
773:
769:
764:
759:
755:
751:
747:
741:
733:
729:
725:
721:
717:
713:
709:
705:
699:
691:
687:
683:
679:
675:
671:
667:
663:
662:Coleman, S.R.
657:
655:
650:
641:
638:
636:
633:
631:
628:
627:
621:
619:
615:
611:
607:
603:
593:
591:
590:quantum group
587:
583:
573:
571:
568:
564:
560:
549:
547:
543:
539:
535:
531:
527:
523:
519:
512:Supersymmetry
509:
507:
503:
499:
495:
491:
476:
473:
472:overdetermine
469:
468:Edward Witten
465:
460:
458:
454:
446:
442:
441:distributions
438:
434:
431:
427:
423:
419:
416:
412:
409:
406:
402:
398:
395:The symmetry
394:
393:
392:
390:
380:
378:
377:string theory
374:
368:
366:
360:
343:
326:
321:
319:
300:
284:
280:
276:
272:
268:
265:
261:
258:model united
242:
211:
195:
194:Eugene Wigner
191:
187:
168:
137:
121:
117:
113:
109:
108:eightfold way
90:
75:
65:
63:
58:
54:
50:
49:supersymmetry
46:
42:
38:
35:and internal
34:
31:stating that
30:
29:no-go theorem
26:
22:
1615:Supergravity
1538:
1508:Localization
1498:Witten index
1473:Moduli space
1367:Superalgebra
1334:Supergravity
1213:
1209:
1203:
1160:
1156:
1150:
1117:
1113:
1103:
1078:
1074:
1064:
1045:
1042:Zichichi, A.
1036:
1017:
1014:Weinberg, S.
980:
976:
959:
940:
934:
909:
905:
892:
867:
863:
853:
834:
821:
802:
796:
753:
749:
740:
715:
711:
698:
673:
669:
599:
580:Models with
579:
555:
530:supercharges
518:Lie algebras
515:
487:
461:
450:
386:
369:
361:
322:
318:relativistic
264:pseudoscalar
118:of the same
71:
24:
18:
1755:Researchers
1741:Stop squark
1706:Graviscalar
1701:Graviphoton
1565:Wess–Zumino
1428:Supercharge
1163:(11): 086.
827:Shifman, M.
666:Mandula, J.
508:generator.
479:Limitations
1867:Categories
1802:Iliopoulos
1746:Superghost
1736:Sgoldstino
1721:Neutralino
1513:Mu problem
1433:R-symmetry
1397:Superspace
1392:Supergroup
1210:J. Phys. A
704:Wigner, E.
635:Supergroup
437:generators
422:amplitudes
37:symmetries
1772:Batchelor
1696:Goldstino
1585:Super QCD
1463:FI D-term
1448:BPS state
1223:0706.3307
1195:119287675
1170:1009.0727
1142:119026420
906:Phys. Rev
763:0902.2201
712:Phys. Rev
670:Phys. Rev
567:tensorial
464:kinematic
401:Lie group
271:multiplet
33:spacetime
1807:Montonen
1731:Sfermion
1726:R-hadron
1711:Higgsino
1686:Chargino
1575:4D N = 1
1532:Theorems
1421:Concepts
1248:15045658
1044:(2012).
965:Haag, R.
900:(1965).
833:(2000).
831:Kane, G.
788:14917968
746:Wess, J.
706:(1937).
624:See also
582:nonlocal
415:energies
389:S-matrix
1822:Seiberg
1797:Golfand
1777:Berezin
1762:Affleck
1691:Gaugino
1228:Bibcode
1175:Bibcode
1122:Bibcode
1083:Bibcode
985:Bibcode
914:Bibcode
872:Bibcode
768:Bibcode
720:Bibcode
678:Bibcode
534:spinors
502:dilaton
494:algebra
426:elastic
383:Theorem
186:flavour
116:hadrons
68:History
1852:Zumino
1847:Witten
1837:Rogers
1827:Siegel
1767:Bagger
1468:F-term
1458:D-term
1246:
1193:
1140:
1052:
1024:
947:
841:
809:
786:
536:under
325:masses
283:quarks
275:baryon
267:mesons
260:vector
74:global
23:, the
1832:Roček
1817:Salam
1812:Olive
1792:Gates
1787:Fayet
1681:Axino
1595:NMSSM
1244:S2CID
1218:arXiv
1191:S2CID
1165:arXiv
1138:S2CID
784:S2CID
758:arXiv
646:Notes
608:with
399:is a
397:group
27:is a
1842:Wess
1782:Dine
1590:MSSM
1161:2010
1157:JHEP
1050:ISBN
1022:ISBN
945:ISBN
839:ISBN
807:ISBN
570:rank
439:are
424:for
420:The
262:and
120:spin
114:for
55:and
47:and
1716:LSP
1236:doi
1183:doi
1130:doi
1118:142
1091:doi
993:doi
922:doi
910:139
880:doi
776:doi
728:doi
686:doi
674:159
443:in
192:by
19:In
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967:;
920:.
908:.
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866:.
862:.
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716:51
714:.
710:.
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664:;
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572:.
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462:A
337:SU
294:SU
236:SU
205:SU
162:SU
131:SU
84:SU
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1297:e
1290:t
1283:v
1250:.
1238::
1230::
1220::
1197:.
1185::
1177::
1167::
1144:.
1132::
1124::
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1093::
1085::
1058:.
1030:.
999:.
995::
987::
953:.
928:.
924::
916::
886:.
882::
874::
847:.
815:.
790:.
778::
770::
760::
734:.
730::
722::
692:.
688::
680::
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417:,
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344:3
341:(
304:)
301:6
298:(
246:)
243:6
240:(
215:)
212:4
209:(
172:)
169:6
166:(
141:)
138:3
135:(
94:)
91:3
88:(
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