46:
899:, the left-moving and the right-moving excitations of strings are completely decoupled, and it is possible to construct a string theory whose left-moving (counter-clockwise) excitations are treated as a bosonic string propagating in
1000:
Because the various superstring theories were shown to be related by dualities, it was proposed that each type of string was a different limit of a single underlying theory called
1665:
1267:
258:
918:
of a linear space). There are two possible even self-dual lattices in 16 dimensions, and it leads to two types of the heterotic string. They differ by the
981:
is a class of symmetries in physics that link different string theories. In the 1990s, it was realized that the strong coupling limit of the HO theory is
818:
1141:
1260:
192:
1632:
1029:
1862:
1597:
197:
2224:
564:
1804:
1310:
1253:
1574:
2249:
1305:
884:
867:
and hence are only of secondary importance in most applications. Heterotic string theory was first developed in 1985 by
589:
1829:
811:
1455:
1750:
1402:
2455:
2089:
2044:
792:
424:
384:
1100:
2269:
2189:
2004:
1938:
1300:
923:
787:
609:
529:
344:
2149:
1771:
1745:
1486:
489:
266:
2409:
2219:
1933:
1776:
1617:
1317:
970:
that would relate the left-moving and the right-moving excitations because they have a different character.
754:
559:
176:
903: = 26 dimensions, while the right-moving (clockwise) excitations are treated as a superstring in
2450:
2174:
1915:
1721:
1612:
1584:
1407:
804:
514:
233:
150:
2324:
1660:
1627:
1491:
1333:
1181:
Adams, Allan; Taylor, Washington; DeWolfe, Oliver (2010-08-10). "String
Universality in Ten Dimensions".
664:
2029:
1969:
1910:
1877:
1872:
1670:
1368:
1363:
1358:
1343:
986:
369:
309:
276:
253:
104:
91:
2199:
539:
2414:
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1054:
982:
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228:
166:
100:
2329:
2214:
1867:
1766:
1392:
1133:
967:
945:
669:
554:
202:
1045:
Gross, David J.; Harvey, Jeffrey A.; Martinec, Emil; Rohm, Ryan (1985-02-11). "Heterotic String".
2374:
2294:
2194:
2154:
2034:
1999:
1834:
1711:
1607:
1348:
1232:
1190:
847:. There are two kinds of heterotic superstring theories, the heterotic SO(32) and the heterotic E
719:
634:
534:
494:
374:
339:
212:
96:
2084:
1761:
694:
2339:
2244:
2079:
1989:
1959:
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1224:
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584:
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329:
299:
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2134:
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1984:
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1954:
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1674:
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1382:
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1125:
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927:
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414:
379:
324:
314:
294:
171:
60:
2429:
2384:
2334:
2319:
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1994:
1564:
1338:
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729:
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649:
544:
509:
334:
238:
2274:
1126:
614:
1204:
1058:
2404:
2399:
2359:
2299:
2289:
2209:
2129:
2119:
2114:
2109:
2024:
2019:
2014:
1979:
1964:
1892:
1569:
1432:
1096:
978:
864:
844:
749:
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704:
639:
629:
549:
469:
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364:
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319:
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207:
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2394:
2379:
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2344:
2314:
2259:
2234:
2179:
2164:
2159:
2124:
2099:
2059:
1849:
1501:
1417:
1295:
1276:
959:
896:
883:(the so-called "Princeton string quartet"), in one of the key papers that fueled the
876:
832:
739:
724:
699:
684:
654:
599:
574:
519:
504:
499:
464:
439:
429:
399:
243:
65:
37:
1236:
45:
2424:
2264:
2144:
2094:
2064:
2049:
1857:
1824:
1716:
1642:
1622:
1559:
1422:
1212:
769:
604:
484:
434:
404:
389:
248:
863:. Apart from that there exist seven more heterotic string theories which are not
2419:
2389:
2369:
2229:
2184:
2139:
2104:
2054:
1819:
1788:
1549:
1506:
919:
868:
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734:
714:
569:
524:
479:
444:
394:
1066:
2364:
2304:
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1902:
1882:
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1740:
1554:
709:
644:
579:
271:
1220:
1151:
1074:
2279:
2069:
2009:
1655:
1529:
1450:
1445:
1440:
994:
990:
880:
619:
409:
349:
135:
130:
125:
28:
1228:
1082:
1925:
1814:
1809:
1539:
1534:
1471:
1387:
1001:
145:
140:
951:
in 10 dimensions. (Although not realized for quite some time, U(1) and E
1544:
1524:
1481:
1476:
75:
17:
27:
This article is about string theory. For heterosis in biology, see
1516:
1195:
839:
is a closed string (or loop) which is a hybrid ('heterotic') of a
70:
1245:
1249:
910:
The mismatched 16 dimensions must be compactified on an even,
1024:. Vol. 2. Cambridge University Press. pp. 55â59.
1132:. Cambridge New York: Cambridge University Press. p.
940:
These two gauge groups also turned out to be the only two
1128:
String theory and M-theory : a modern introduction
1947:
1924:
1901:
1848:
1733:
1641:
1583:
1515:
1464:
1431:
1326:
1283:
1124:Becker, Katrin; Becker, M.; Schwarz, J. H. (2007).
1101:"String theory, at 20, explains it all (or not)"
1053:(6). American Physical Society (APS): 502â505.
944:-free gauge groups that can be coupled to the
1261:
993:. The HO and HE theories are also related by
812:
8:
1022:String Theory: Superstring Theory and Beyond
1268:
1254:
1246:
819:
805:
44:
33:
1194:
1012:
184:
158:
117:
83:
52:
36:
922:in 10 dimensions. One gauge group is
7:
1666:Bogomol'nyiâPrasadâSommerfield bound
985:— a theory that also contains
262:= 4 supersymmetric YangâMills theory
966:; it is not possible to define any
926:(the HO string) while the other is
955: Ă U(1) are anomalous.)
193:Geometric Langlands correspondence
25:
958:Every heterotic string must be a
1863:Eleven-dimensional supergravity
1213:10.1103/physrevlett.105.071601
1:
1311:Second superstring revolution
1805:Generalized complex manifold
1306:First superstring revolution
907: = 10 dimensions.
885:first superstring revolution
1020:Polchinski, Joseph (1998).
949: = 1 supergravity
2472:
1403:Non-critical string theory
1067:10.1103/physrevlett.54.502
989:; this relation is called
26:
1939:Introduction to M-theory
1633:WessâZuminoâWitten model
1575:HananyâWitten transition
1301:History of string theory
118:Non-perturbative results
1618:Vertex operator algebra
1318:String theory landscape
1183:Physical Review Letters
1169:String Theory: Volume 2
1047:Physical Review Letters
1916:AdS/CFT correspondence
1671:Exceptional Lie groups
1613:Superconformal algebra
1585:Conformal field theory
1456:MontonenâOlive duality
1408:Non-linear sigma model
234:Conformal field theory
151:AdS/CFT correspondence
1911:Holographic principle
1878:Type IIB supergravity
1873:Type IIA supergravity
1725:-form electrodynamics
1344:Bosonic string theory
277:Holographic principle
254:Twistor string theory
1830:HoĆavaâWitten theory
1777:HyperkÀhler manifold
1465:Particles and fields
1413:Tachyon condensation
1398:Matrix string theory
983:type I string theory
229:Theory of everything
1868:Type I supergravity
1772:CalabiâYau manifold
1767:Ricci-flat manifold
1746:KaluzaâKlein theory
1487:RamondâRamond field
1393:String field theory
1205:2010PhRvL.105g1601A
1059:1985PhRvL..54..502G
968:boundary conditions
267:KaluzaâKlein theory
203:Monstrous moonshine
84:Perturbative theory
53:Fundamental objects
1835:K-theory (physics)
1712:ADE classification
1349:Superstring theory
1105:The New York Times
2438:
2437:
2220:van Nieuwenhuizen
1756:Why 10 dimensions
1661:ChernâSimons form
1628:KacâMoody algebra
1608:Conformal algebra
1603:Conformal anomaly
1497:Magnetic monopole
1492:KalbâRamond field
1334:NambuâGoto action
1165:Joseph Polchinski
1143:978-0-521-86069-7
937:(the HE string).
916:discrete subgroup
912:self-dual lattice
855:, abbreviated to
829:
828:
560:van Nieuwenhuizen
16:(Redirected from
2463:
2456:E8 (mathematics)
1948:String theorists
1888:Lie superalgebra
1840:Twisted K-theory
1798:Spin(7)-manifold
1751:Compactification
1593:Virasoro algebra
1376:Heterotic string
1270:
1263:
1256:
1247:
1241:
1240:
1198:
1178:
1172:
1162:
1156:
1155:
1131:
1121:
1115:
1114:
1112:
1111:
1093:
1087:
1086:
1042:
1036:
1035:
1017:
837:heterotic string
821:
814:
807:
223:Related concepts
48:
34:
21:
2471:
2470:
2466:
2465:
2464:
2462:
2461:
2460:
2441:
2440:
2439:
2434:
1943:
1920:
1897:
1844:
1792:
1762:KĂ€hler manifold
1729:
1706:
1699:
1692:
1685:
1678:
1637:
1598:Mirror symmetry
1579:
1565:Brane cosmology
1511:
1460:
1427:
1383:N=2 superstring
1369:Type IIB string
1364:Type IIA string
1339:Polyakov action
1322:
1279:
1274:
1244:
1180:
1179:
1175:
1163:
1159:
1144:
1123:
1122:
1118:
1109:
1107:
1095:
1094:
1090:
1044:
1043:
1039:
1032:
1019:
1018:
1014:
1010:
976:
954:
935:
931:
893:
854:
850:
825:
780:
779:
290:
282:
281:
239:Quantum gravity
224:
198:Mirror symmetry
32:
23:
22:
15:
12:
11:
5:
2469:
2467:
2459:
2458:
2453:
2443:
2442:
2436:
2435:
2433:
2432:
2427:
2422:
2417:
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2407:
2402:
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2392:
2387:
2382:
2377:
2372:
2367:
2362:
2357:
2352:
2347:
2342:
2337:
2332:
2327:
2322:
2317:
2312:
2307:
2302:
2297:
2292:
2287:
2282:
2277:
2272:
2270:Randjbar-Daemi
2267:
2262:
2257:
2252:
2247:
2242:
2237:
2232:
2227:
2222:
2217:
2212:
2207:
2202:
2197:
2192:
2187:
2182:
2177:
2172:
2167:
2162:
2157:
2152:
2147:
2142:
2137:
2132:
2127:
2122:
2117:
2112:
2107:
2102:
2097:
2092:
2087:
2082:
2077:
2072:
2067:
2062:
2057:
2052:
2047:
2042:
2037:
2032:
2027:
2022:
2017:
2012:
2007:
2002:
1997:
1992:
1987:
1982:
1977:
1972:
1967:
1962:
1957:
1951:
1949:
1945:
1944:
1942:
1941:
1936:
1930:
1928:
1922:
1921:
1919:
1918:
1913:
1907:
1905:
1899:
1898:
1896:
1895:
1893:Lie supergroup
1890:
1885:
1880:
1875:
1870:
1865:
1860:
1854:
1852:
1846:
1845:
1843:
1842:
1837:
1832:
1827:
1822:
1817:
1812:
1807:
1802:
1801:
1800:
1795:
1790:
1786:
1785:
1784:
1774:
1764:
1759:
1753:
1748:
1743:
1737:
1735:
1731:
1730:
1728:
1727:
1719:
1714:
1709:
1704:
1697:
1690:
1683:
1676:
1668:
1663:
1658:
1653:
1647:
1645:
1639:
1638:
1636:
1635:
1630:
1625:
1620:
1615:
1610:
1605:
1600:
1595:
1589:
1587:
1581:
1580:
1578:
1577:
1572:
1570:Quiver diagram
1567:
1562:
1557:
1552:
1547:
1542:
1537:
1532:
1527:
1521:
1519:
1513:
1512:
1510:
1509:
1504:
1499:
1494:
1489:
1484:
1479:
1474:
1468:
1466:
1462:
1461:
1459:
1458:
1453:
1448:
1443:
1437:
1435:
1433:String duality
1429:
1428:
1426:
1425:
1420:
1415:
1410:
1405:
1400:
1395:
1390:
1385:
1380:
1379:
1378:
1373:
1372:
1371:
1366:
1359:Type II string
1356:
1346:
1341:
1336:
1330:
1328:
1324:
1323:
1321:
1320:
1315:
1314:
1313:
1308:
1298:
1296:Cosmic strings
1293:
1287:
1285:
1281:
1280:
1275:
1273:
1272:
1265:
1258:
1250:
1243:
1242:
1173:
1157:
1142:
1116:
1099:(2004-12-07).
1097:Dennis Overbye
1088:
1037:
1030:
1011:
1009:
1006:
979:String duality
975:
974:String duality
972:
952:
933:
932: Ă E
929:
892:
889:
873:Jeffrey Harvey
865:supersymmetric
852:
851: Ă E
848:
845:bosonic string
827:
826:
824:
823:
816:
809:
801:
798:
797:
796:
795:
790:
782:
781:
778:
777:
772:
767:
762:
757:
752:
747:
742:
737:
732:
727:
722:
717:
712:
707:
702:
697:
692:
687:
682:
677:
672:
667:
662:
657:
652:
647:
642:
637:
632:
627:
622:
617:
612:
610:Randjbar-Daemi
607:
602:
597:
592:
587:
582:
577:
572:
567:
562:
557:
552:
547:
542:
537:
532:
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512:
507:
502:
497:
492:
487:
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477:
472:
467:
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457:
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402:
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352:
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312:
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297:
291:
288:
287:
284:
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269:
264:
256:
251:
246:
241:
236:
231:
225:
222:
221:
218:
217:
216:
215:
210:
208:Vertex algebra
205:
200:
195:
187:
186:
182:
181:
180:
179:
174:
169:
161:
160:
156:
155:
154:
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148:
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138:
133:
128:
120:
119:
115:
114:
113:
112:
94:
86:
85:
81:
80:
79:
78:
73:
68:
63:
55:
54:
50:
49:
41:
40:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2468:
2457:
2454:
2452:
2451:String theory
2449:
2448:
2446:
2431:
2428:
2426:
2423:
2421:
2418:
2416:
2415:Zamolodchikov
2413:
2411:
2410:Zamolodchikov
2408:
2406:
2403:
2401:
2398:
2396:
2393:
2391:
2388:
2386:
2383:
2381:
2378:
2376:
2373:
2371:
2368:
2366:
2363:
2361:
2358:
2356:
2353:
2351:
2348:
2346:
2343:
2341:
2338:
2336:
2333:
2331:
2328:
2326:
2323:
2321:
2318:
2316:
2313:
2311:
2308:
2306:
2303:
2301:
2298:
2296:
2293:
2291:
2288:
2286:
2283:
2281:
2278:
2276:
2273:
2271:
2268:
2266:
2263:
2261:
2258:
2256:
2253:
2251:
2248:
2246:
2243:
2241:
2238:
2236:
2233:
2231:
2228:
2226:
2223:
2221:
2218:
2216:
2213:
2211:
2208:
2206:
2203:
2201:
2198:
2196:
2193:
2191:
2188:
2186:
2183:
2181:
2178:
2176:
2173:
2171:
2168:
2166:
2163:
2161:
2158:
2156:
2153:
2151:
2148:
2146:
2143:
2141:
2138:
2136:
2133:
2131:
2128:
2126:
2123:
2121:
2118:
2116:
2113:
2111:
2108:
2106:
2103:
2101:
2098:
2096:
2093:
2091:
2088:
2086:
2083:
2081:
2078:
2076:
2073:
2071:
2068:
2066:
2063:
2061:
2058:
2056:
2053:
2051:
2048:
2046:
2043:
2041:
2038:
2036:
2033:
2031:
2028:
2026:
2023:
2021:
2018:
2016:
2013:
2011:
2008:
2006:
2003:
2001:
1998:
1996:
1993:
1991:
1988:
1986:
1983:
1981:
1978:
1976:
1973:
1971:
1968:
1966:
1963:
1961:
1958:
1956:
1953:
1952:
1950:
1946:
1940:
1937:
1935:
1934:Matrix theory
1932:
1931:
1929:
1927:
1923:
1917:
1914:
1912:
1909:
1908:
1906:
1904:
1900:
1894:
1891:
1889:
1886:
1884:
1881:
1879:
1876:
1874:
1871:
1869:
1866:
1864:
1861:
1859:
1856:
1855:
1853:
1851:
1850:Supersymmetry
1847:
1841:
1838:
1836:
1833:
1831:
1828:
1826:
1823:
1821:
1818:
1816:
1813:
1811:
1808:
1806:
1803:
1799:
1796:
1794:
1787:
1783:
1780:
1779:
1778:
1775:
1773:
1770:
1769:
1768:
1765:
1763:
1760:
1757:
1754:
1752:
1749:
1747:
1744:
1742:
1739:
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1736:
1732:
1726:
1724:
1720:
1718:
1715:
1713:
1710:
1707:
1700:
1693:
1686:
1679:
1672:
1669:
1667:
1664:
1662:
1659:
1657:
1654:
1652:
1649:
1648:
1646:
1644:
1640:
1634:
1631:
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1502:Dual graviton
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1277:String theory
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1189:(7): 071601.
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960:closed string
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897:string theory
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877:Emil Martinec
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833:string theory
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167:Phenomenology
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159:Phenomenology
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66:Cosmic string
64:
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59:
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56:
51:
47:
43:
42:
39:
38:String theory
35:
30:
19:
1960:Arkani-Hamed
1858:Supergravity
1825:Moduli space
1722:
1717:Dirac string
1643:Gauge theory
1623:Loop algebra
1560:Black string
1423:GS formalism
1375:
1186:
1182:
1176:
1168:
1160:
1127:
1119:
1108:. Retrieved
1104:
1091:
1050:
1046:
1040:
1021:
1015:
999:
987:open strings
977:
957:
946:
939:
909:
904:
900:
894:
860:
856:
836:
830:
300:Arkani-Hamed
259:
249:Supergravity
108:
2320:Silverstein
1820:Orientifold
1555:Black holes
1550:Black brane
1507:Dual photon
964:open string
920:gauge group
869:David Gross
841:superstring
660:Silverstein
185:Mathematics
97:Superstring
2445:Categories
2340:Strominger
2335:Steinhardt
2330:Staudacher
2245:Polchinski
2195:Nanopoulos
2155:Mandelstam
2135:Kontsevich
1975:Berenstein
1903:Holography
1883:Superspace
1782:K3 surface
1741:Worldsheet
1656:Instantons
1284:Background
1110:2020-03-15
1008:References
680:Strominger
675:Steinhardt
670:Staudacher
585:Polchinski
535:Nanopoulos
495:Mandelstam
475:Kontsevich
315:Berenstein
272:Multiverse
2375:Veneziano
2255:Rajaraman
2150:Maldacena
2040:Gopakumar
1990:Dijkgraaf
1985:Curtright
1651:Anomalies
1530:NS5-brane
1451:U-duality
1446:S-duality
1441:T-duality
1221:0031-9007
1196:1006.1352
1152:607562796
1075:0031-9007
995:T-duality
991:S-duality
962:, not an
881:Ryan Rohm
720:Veneziano
595:Rajaraman
490:Maldacena
380:Gopakumar
330:Dijkgraaf
325:Curtright
289:Theorists
177:Landscape
172:Cosmology
136:U-duality
131:T-duality
126:S-duality
109:Heterotic
29:Heterosis
2430:Zwiebach
2385:Verlinde
2380:Verlinde
2355:Townsend
2350:Susskind
2285:Sagnotti
2250:Polyakov
2205:Nekrasov
2170:Minwalla
2165:Martinec
2130:Knizhnik
2125:Klebanov
2120:Kapustin
2085:'t Hooft
2020:Fischler
1955:AganagiÄ
1926:M-theory
1815:Conifold
1810:Orbifold
1793:manifold
1734:Geometry
1540:M5-brane
1535:M2-brane
1472:Graviton
1388:F-theory
1237:13916249
1229:20868028
1171:, p. 45.
1167:(1998).
1083:10031535
1002:M-theory
891:Overview
793:Glossary
775:Zwiebach
730:Verlinde
725:Verlinde
700:Townsend
695:'t Hooft
690:Susskind
625:Sagnotti
590:Polyakov
545:Nekrasov
510:Minwalla
505:Martinec
470:Knizhnik
465:Klebanov
460:Kapustin
430:Horowitz
360:Fischler
295:AganagiÄ
213:K-theory
146:F-theory
141:M-theory
2360:Trivedi
2345:Sundrum
2310:Shenker
2300:Seiberg
2295:Schwarz
2265:Randall
2225:Novikov
2215:Nielsen
2200:NÄstase
2110:Kallosh
2095:Gibbons
2035:Gliozzi
2025:Friedan
2015:Ferrara
2000:Douglas
1995:Distler
1545:S-brane
1525:D-brane
1482:Tachyon
1477:Dilaton
1291:Strings
1201:Bibcode
1055:Bibcode
942:anomaly
788:History
705:Trivedi
685:Sundrum
650:Shenker
640:Seiberg
635:Schwarz
605:Randall
565:Novikov
555:Nielsen
540:NÄstase
450:Kallosh
435:Gibbons
375:Gliozzi
365:Friedan
355:Ferrara
340:Douglas
335:Distler
105:Type II
92:Bosonic
76:D-brane
2425:Zumino
2420:Zaslow
2405:Yoneya
2395:Witten
2315:Siegel
2290:Scherk
2260:Ramond
2235:Ooguri
2160:Marolf
2115:Kaluza
2100:Kachru
2090:HoĆava
2080:Harvey
2075:Hanson
2060:Gubser
2050:Greene
1980:Bousso
1965:Atiyah
1517:Branes
1327:Theory
1235:
1227:
1219:
1150:
1140:
1081:
1073:
1028:
924:SO(32)
879:, and
843:and a
770:Zumino
765:Zaslow
750:Yoneya
740:Witten
655:Siegel
630:Scherk
600:Ramond
575:Ooguri
500:Marolf
455:Kaluza
440:Kachru
425:HoĆava
420:Harvey
415:Hanson
400:Gubser
390:Greene
320:Bousso
305:Atiyah
101:Type I
61:String
18:SO(32)
2365:Turok
2275:RoÄek
2240:Ovrut
2230:Olive
2210:Neveu
2190:Myers
2185:Mukhi
2175:Moore
2145:Linde
2140:Klein
2065:Gukov
2055:Gross
2045:Green
2030:Gates
2010:Dvali
1970:Banks
1233:S2CID
1191:arXiv
710:Turok
615:RoÄek
580:Ovrut
570:Olive
550:Neveu
530:Myers
525:Mukhi
515:Moore
485:Linde
480:Klein
405:Gukov
395:Gross
385:Green
370:Gates
350:Dvali
310:Banks
71:Brane
2390:Wess
2370:Vafa
2280:Rohm
2180:Motl
2105:Kaku
2070:Guth
2005:Duff
1225:PMID
1217:ISSN
1148:OCLC
1138:ISBN
1079:PMID
1071:ISSN
1026:ISBN
859:and
835:, a
735:Wess
715:Vafa
620:Rohm
520:Motl
445:Kaku
410:Guth
345:Duff
2400:Yau
2325:SÆĄn
2305:Sen
1209:doi
1187:105
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831:In
745:Yau
665:SÆĄn
645:Sen
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