31:
935:
s TV version, in the second episode, "The String's the Thing", section "Wrestling with String Theory", Green describes finding 496 on each side of the equals sign during a stormy night filled with lightning, and fondly recalls joking that "the gods are trying to prevent us from completing this
1056:
1122:
1249:
917:, this indeed occurs. The tree diagram describes the exchange of a virtual quantum of the B-field. It is somewhat counterintuitive to see that a tree diagram cancels a
1309:
1339:
1276:
1180:
1149:
952:, or global symmetry currents as the external legs. These diagrams have the form of a triangle in 4 spacetime dimensions, which generalizes to a hexagon in
243:
803:
1341:, when combined with a trilinear vertex through exchange of a gauge boson, has precisely the right variation to cancel the hexagon anomaly.
1251:(with space-time indices not contracted), which is precisely one of the factors appearing in the hexagon anomaly. If the variation of
177:
963:= 10 gauge theory is the hexagon which has a particular linear combination of the two-form gauge field strength and Ricci tensor,
182:
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Anomalies in quantum theory arise from one-loop diagrams, with a chiral fermion in the loop and gauge fields,
474:
251:
867:
field. They realized that one of the necessary conditions for a superstring theory to make sense is that the
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and under general coordinate transformations is appropriately specified, then the Green–Schwarz term
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1365:(1984). "Anomaly cancellations in supersymmetric D = 10 gauge theory and superstring theory".
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1416:
Frampton, P.; Kephart, T. (1983). "Explicit
Evaluation of Anomalies in Higher Dimensions".
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913:, however, the anomaly factorizes and may be cancelled by a tree diagram. In
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120:
115:
110:
130:
125:
921:, but in reality, both of these diagrams arise as one-loop diagrams in
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936:
calculation". Green soon entitled some of his subsequent lectures "
956:= 10, thus involving 6 external lines. The interesting anomaly in
55:
957:
863:
cancels because of an extra "classical" contribution from a
1061:
Green and
Schwarz realized that one can add a so-called
1051:{\displaystyle F^{6},\ F^{4}R^{2},\ F^{2}R^{4},\ R^{6}}
925:
in which the anomaly cancellation is more transparent.
1317:
1284:
1257:
1188:
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1130:
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969:
1406:, Cambridge University Press, 2003, section 7.1.4.
1333:
1303:
1270:
1243:
1174:
1143:
1116:
1050:
1124:, where the integral is over the 10 dimensions,
1065:term to the classical action, having the form
1278:under the transformations of gauge field for
1117:{\displaystyle S_{GS}=\int B_{2}\wedge X_{8}}
797:
8:
822:Green–Schwarz anomaly cancellation mechanism
1244:{\displaystyle F^{4},\ F^{2}R^{2},\ R^{4}}
804:
790:
29:
18:
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1316:
1289:
1283:
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1129:
1108:
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1016:
1000:
990:
974:
968:
824:) is the main discovery that started the
1350:
169:
143:
102:
68:
37:
21:
1182:is a gauge invariant combination of
883:and then demonstrated this to be so.
7:
247:= 4 supersymmetric Yang–Mills theory
178:Geometric Langlands correspondence
14:
905:. For the special choice of the
16:Mechanism in superstring theory
1296:
1290:
898:were expected to arise from a
1:
886:In the original calculation,
1387:10.1016/0370-2693(84)91565-X
826:first superstring revolution
1438:10.1103/PhysRevLett.50.1343
1484:
1058:, for the external lines.
938:The Theory of Everything
103:Non-perturbative results
1418:Physical Review Letters
1304:{\displaystyle F_{(2)}}
896:gravitational anomalies
818:Green–Schwarz mechanism
1335:
1334:{\displaystyle S_{GS}}
1305:
1272:
1245:
1176:
1145:
1118:
1052:
820:(sometimes called the
219:Conformal field theory
136:AdS/CFT correspondence
1336:
1306:
1273:
1271:{\displaystyle B_{2}}
1246:
1177:
1175:{\displaystyle X_{8}}
1146:
1144:{\displaystyle B_{2}}
1119:
1053:
262:Holographic principle
239:Twistor string theory
1315:
1282:
1255:
1186:
1159:
1128:
1069:
967:
931:The Elegant Universe
877:type I string theory
854:type I string theory
214:Theory of everything
1458:Anomalies (physics)
1430:1983PhRvL..50.1343F
1400:Clifford V. Johnson
1379:1984PhLB..149..117G
252:Kaluza–Klein theory
188:Monstrous moonshine
69:Perturbative theory
38:Fundamental objects
1331:
1301:
1268:
1241:
1172:
1141:
1114:
1048:
923:superstring theory
848:realized that the
830:superstring theory
1367:Physics Letters B
1230:
1204:
1153:Kalb–Ramond field
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1011:
985:
814:
813:
545:van Nieuwenhuizen
1475:
1442:
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1373:(1–3): 117–122.
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1151:is the rank-two
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1005:
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928:As recounted in
919:one-loop diagram
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792:
208:Related concepts
33:
19:
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1463:Quantum gravity
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903:Feynman diagram
892:mixed anomalies
888:gauge anomalies
846:John H. Schwarz
838:
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765:
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275:
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224:Quantum gravity
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183:Mirror symmetry
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12:
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5:
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1363:Schwarz, J. H.
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595:Randjbar-Daemi
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193:Vertex algebra
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1468:String theory
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950:Ricci tensors
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915:string theory
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842:Michael Green
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745:Zamolodchikov
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740:Zamolodchikov
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229:Supersymmetry
227:
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152:Phenomenology
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149:
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144:Phenomenology
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127:
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119:
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67:
62:
59:
57:
54:
52:
51:Cosmic string
49:
47:
44:
43:
42:
41:
36:
32:
28:
27:
24:
23:String theory
20:
1424:(18): 1343.
1421:
1417:
1411:
1403:
1395:
1370:
1366:
1359:Green, M. B.
1353:
1063:Chern–Simons
1060:
960:
953:
947:
929:
927:
885:
839:
821:
817:
815:
285:Arkani-Hamed
244:
234:Supergravity
907:gauge group
873:gauge group
858:gauge group
645:Silverstein
170:Mathematics
82:Superstring
1452:Categories
1345:References
909:SO(32) or
665:Strominger
660:Steinhardt
655:Staudacher
570:Polchinski
520:Nanopoulos
480:Mandelstam
460:Kontsevich
300:Berenstein
257:Multiverse
1102:∧
1089:∫
869:dimension
856:with the
840:In 1984,
836:Discovery
705:Veneziano
580:Rajaraman
475:Maldacena
365:Gopakumar
315:Dijkgraaf
310:Curtright
274:Theorists
162:Landscape
157:Cosmology
121:U-duality
116:T-duality
111:S-duality
94:Heterotic
1404:D-branes
879:must be
778:Glossary
760:Zwiebach
715:Verlinde
710:Verlinde
685:Townsend
680:'t Hooft
675:Susskind
610:Sagnotti
575:Polyakov
530:Nekrasov
495:Minwalla
490:Martinec
455:Knizhnik
450:Klebanov
445:Kapustin
415:Horowitz
345:Fischler
280:Aganagić
198:K-theory
131:F-theory
126:M-theory
1426:Bibcode
1375:Bibcode
944:Details
911:E8 x E8
900:hexagon
871:of the
850:anomaly
773:History
690:Trivedi
670:Sundrum
635:Shenker
625:Seiberg
620:Schwarz
590:Randall
550:Novikov
540:Nielsen
525:Năstase
435:Kallosh
420:Gibbons
360:Gliozzi
350:Friedan
340:Ferrara
325:Douglas
320:Distler
90:Type II
77:Bosonic
61:D-brane
1229:
1203:
1155:, and
1036:
1010:
984:
894:, and
865:2-form
861:SO(32)
755:Zumino
750:Zaslow
735:Yoneya
725:Witten
640:Siegel
615:Scherk
585:Ramond
560:Ooguri
485:Marolf
440:Kaluza
425:Kachru
410:Hořava
405:Harvey
400:Hanson
385:Gubser
375:Greene
305:Bousso
290:Atiyah
86:Type I
46:String
695:Turok
600:Roček
565:Ovrut
555:Olive
535:Neveu
515:Myers
510:Mukhi
500:Moore
470:Linde
465:Klein
390:Gukov
380:Gross
370:Green
355:Gates
335:Dvali
295:Banks
56:Brane
958:SUSY
844:and
816:The
720:Wess
700:Vafa
605:Rohm
505:Motl
430:Kaku
395:Guth
330:Duff
1434:doi
1383:doi
1371:149
940:".
881:496
875:of
852:in
828:in
730:Yau
650:Sơn
630:Sen
1454::
1432:.
1422:50
1420:.
1402:,
1381:.
1369:.
1361:;
890:,
832:.
92:,
88:,
1440:.
1436::
1428::
1389:.
1385::
1377::
1327:S
1324:G
1320:S
1297:)
1294:2
1291:(
1287:F
1264:2
1260:B
1237:4
1233:R
1226:,
1221:2
1217:R
1211:2
1207:F
1200:,
1195:4
1191:F
1168:8
1164:X
1137:2
1133:B
1110:8
1106:X
1097:2
1093:B
1086:=
1081:S
1078:G
1074:S
1044:6
1040:R
1033:,
1028:4
1024:R
1018:2
1014:F
1007:,
1002:2
998:R
992:4
988:F
981:,
976:6
972:F
961:D
954:D
933:'
805:e
798:t
791:v
245:N
96:)
84:(
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