1717:
atomic principle)). Combining these effects with a mild power-law draw to large soft SUSY breaking terms, one may calculate the Higgs boson and superparticle masses expected from the landscape. The Higgs mass probability distribution peaks around 125 GeV while sparticles (with the exception of light higgsinos) tend to lie well beyond current LHC search limits. This approach is an example of the application of stringy naturalness.
42:
1526:
A problem with many of the simplified approaches people have tried is that they "predict" a cosmological constant that is too large by a factor of 10â1000 orders of magnitude (depending on one's assumptions) and hence suggest that the cosmic acceleration should be much more rapid than is observed.
1716:
is the number of D-breaking fields (distributed as real numbers). Next, one may impose the
Agrawal, Barr, Donoghue, Seckel (ABDS) anthropic requirement that the derived weak scale lie within a factor of a few of our measured value (lest nuclei as needed for life as we know it become unstable (the
1566:
The string landscape ideas can be applied to the notion of weak scale supersymmetry and the Little
Hierarchy problem. For string vacua which include the MSSM (Minimal Supersymmetric Standard Model) as the low energy effective field theory, all values of SUSY breaking fields are expected to be
1497:
is completely unknown, since so little is known about the origin of life. Simplified criteria (such as the number of galaxies) must be used as a proxy for the number of observers. Moreover, it may never be possible to compute it for parameters radically different from those of the observable
1254:
1029:
mass are usually assumed to occur for precise physical reasons as opposed to taking their particular values at random. That is, these values should be uniquely consistent with underlying physical laws.
1660:
1066:
Weinberg attempted to predict the magnitude of the cosmological constant based on probabilistic arguments. Other attempts have been made to apply similar reasoning to models of particle physics.
1495:
1371:
1439:
1298:
1037:
proposes that fundamental constants may have the values they have because such values are necessary for life (and therefore intelligent observers to measure the constants). The
948:
2942:
915:
1714:
1687:
1115:
2544:
1033:
The number of theoretically allowed configurations has prompted suggestions that this is not the case, and that many different vacua are physically realized. The
1391:
1318:
1135:
2375:
V. Agrawal, S. M. Barr, J. F. Donoghue and D. Seckel, "Anthropic considerations in multiple domain theories and the scale of electroweak symmetry breaking",
1535:
Few dispute the large number of metastable vacua. The existence, meaning, and scientific relevance of the anthropic landscape, however, remain controversial.
254:
2476:; GarcĂa-Etxebarria, Iñaki; Halverson, James (March 2011). "On the computation of non-perturbative effective potentials in the string theory landscape".
1143:
1567:
equally likely on the landscape. This led
Douglas and others to propose that the SUSY breaking scale is distributed as a power law in the landscape
1728:
suggests that the idea is inherently unscientific, unfalsifiable or premature. A famous debate on the anthropic landscape of string theory is the
814:
1396:
These probabilistic arguments are the most controversial aspect of the landscape. Technical criticisms of these proposals have pointed out that:
1827:
2537:
188:
2909:
1373:
is the "anthropic selection function", determined by the number of "observers" that would occur in the universe with parameters
3139:
2874:
193:
969:
If there is no structure in the space of vacua, the problem of finding one with a sufficiently small cosmological constant is
3501:
1570:
560:
3081:
2587:
2530:
2462:
1555:
2851:
3526:
2582:
585:
3106:
3727:
1441:
is completely unknown in string theory and may be impossible to define or interpret in any sensible probabilistic way.
807:
2732:
1729:
1041:
thus refers to the collection of those portions of the landscape that are suitable for supporting intelligent life.
3027:
2679:
881:
844:
3366:
3321:
788:
420:
380:
1063:
was so small because it is impossible for life to occur in a universe with a much larger cosmological constant.
3546:
3466:
3281:
3215:
2577:
2012:
Kachru, Shamit; Kallosh, Renata; Linde, Andrei; Trivedi, Sandip P. (2003). "de Sitter Vacua in String Theory".
1078:
783:
605:
525:
340:
3426:
3048:
3022:
2763:
1740:
There are several popular books about the anthropic principle in cosmology. The authors of two physics blogs,
1447:
1323:
951:
485:
262:
2114:
M. Tegmark, A. Aguirre, M. Rees and F. Wilczek, "Dimensionless constants, cosmology and other dark matters",
3686:
3496:
3210:
3053:
2894:
2652:
2306:
Delia
Schwartz-Perlov & Alexander Vilenkin (2006). "Probabilities in the Bousso-Polchinski multiverse".
1780:
The number of metastable vacua is not known exactly, but commonly quoted estimates are of the order 10. See
1082:
750:
555:
104:
3732:
3451:
3192:
2998:
2889:
2861:
2684:
2398:
H. Baer, V. Barger, H. Serce and K. Sinha, "Higgs and superparticle mass predictions from the landscape",
1851:
1523:
Vilenkin and collaborators have proposed a consistent way to define the probabilities for a given vacuum.
1403:
1262:
959:
864:
800:
510:
229:
146:
3601:
2937:
2904:
2768:
2610:
660:
3306:
3246:
3187:
3154:
3149:
2947:
2645:
2640:
2635:
2620:
2253:
Jaume
Garriga & Alexander Vilenkin (2006). "Anthropic prediction for Lambda and the Q catastrophe".
1060:
1022:
1018:
1009:
365:
305:
272:
249:
100:
87:
3476:
535:
3691:
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2166:
2031:
1978:
1925:
1070:
1050:
855:
755:
224:
162:
96:
2200:
Abraham Loeb (2006). "An observational test for the anthropic origin of the cosmological constant".
1819:
Quantum Space Loop
Quantum Gravity and the Search for the Structure of Space, Time, and the Universe
1085:
but not in
Bayesian probability, which is not defined in terms of the frequency of repeated events.
3737:
3606:
3491:
3144:
3043:
2669:
1757:
1034:
1013:
665:
550:
198:
920:
3651:
3571:
3471:
3431:
3311:
3276:
3111:
2988:
2884:
2625:
2511:
2485:
2406:
2383:
2359:
2341:
2315:
2288:
2262:
2235:
2209:
2182:
2156:
2123:
2115:
2098:
2065:
2047:
2021:
1994:
1968:
1941:
1915:
1888:
1792:
1781:
974:
715:
630:
530:
490:
370:
335:
208:
92:
3361:
3038:
887:
690:
3616:
3521:
3356:
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3032:
2927:
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1823:
1817:
893:
851:
675:
580:
415:
325:
295:
3626:
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3531:
3411:
3351:
3316:
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3251:
3231:
3164:
3116:
3074:
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2958:
2951:
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2659:
2567:
2503:
2473:
2333:
2280:
2227:
2174:
2039:
1986:
1933:
1878:
1551:
869:
685:
620:
590:
470:
410:
375:
320:
310:
290:
167:
56:
1692:
1665:
1513:
have recently considered these objections and proposed a simplified anthropic scenario for
3706:
3661:
3611:
3596:
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3481:
3446:
3271:
2841:
2615:
1547:
1091:
1056:
770:
725:
670:
655:
645:
540:
505:
330:
234:
3551:
1959:
Frederik Denef; Douglas, Michael R. (2007). "Computational complexity of the landscape".
610:
2499:
2337:
2329:
2276:
2231:
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2170:
2035:
1982:
1929:
3681:
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3391:
3386:
3301:
3296:
3291:
3256:
3241:
3169:
2846:
2709:
1906:
Taylor, Washington; Wang, Yi-Nan (2015). "The F-theory geometry with most flux vacua".
1376:
1303:
1120:
997:
989:
745:
740:
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635:
625:
545:
465:
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360:
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315:
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203:
2178:
2131:
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3401:
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3336:
3126:
2778:
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2553:
2345:
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2051:
1892:
1762:
985:
955:
828:
735:
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695:
680:
650:
595:
570:
515:
500:
495:
460:
435:
425:
395:
239:
61:
33:
2515:
2239:
1945:
41:
17:
3701:
3541:
3421:
3371:
3341:
3326:
3134:
3101:
2993:
2919:
2899:
2836:
2699:
1543:
993:
840:
765:
600:
480:
430:
400:
385:
244:
1998:
843:, together comprising a collective "landscape" of choices of parameters governing
2430:(Basic Books, 2001). R. Bousso and J. Polchinski, "The string theory landscape",
3696:
3666:
3646:
3506:
3461:
3416:
3381:
3331:
3096:
3065:
2826:
2783:
1937:
1725:
1517:
1507:
1074:
1026:
970:
760:
730:
710:
565:
520:
475:
440:
390:
2043:
1883:
1866:
1249:{\displaystyle P(x)=P_{\mathrm {prior} }(x)\times P_{\mathrm {selection} }(x),}
3641:
3581:
3516:
3179:
3159:
3058:
3017:
2831:
1990:
1745:
1741:
1073:; interpreting probability in a context where it is only possible to draw one
859:
705:
640:
575:
267:
980:
A possible mechanism of string theory vacuum stabilization, now known as the
3556:
3346:
3286:
2932:
2806:
2727:
2722:
2717:
2466:
615:
405:
345:
131:
126:
121:
2507:
2447:
2358:
M. R. Douglas, "Statistical analysis of the supersymmetry breaking scale",
2424:
The cosmic landscape: string theory and the illusion of intelligent design
3202:
3091:
3086:
2816:
2811:
2748:
2664:
2463:
String landscape; moduli stabilization; flux vacua; flux compactification
2284:
2214:
2119:
1689:
is the number of F-breaking fields (distributed as complex numbers) and
963:
141:
136:
2821:
2801:
2758:
2753:
2387:
2363:
2320:
2267:
2161:
2127:
2102:
2069:
2026:
1973:
1796:
1520:
in which they argue that the first two of these problems do not apply.
71:
1300:
is the prior probability, from fundamental theory, of the parameters
950:
or higher. The large number of possibilities arises from choices of
2410:
1920:
2793:
2490:
1514:
66:
2122:. F. Wilczek, "Enlightenment, knowledge, ignorance, temptation",
2522:
2526:
868:(1997), and was first used in the context of string theory by
2081:
S. Weinberg, "Anthropic bound on the cosmological constant",
2446:
Motl's blog criticized the anthropic principle and Woit's
2147:
Alexander
Vilenkin (2007). "A measure of the multiverse".
2428:
Just six numbers: the deep forces that shape the universe
2064:
L. Susskind, "The anthropic landscape of string theory",
2105:
reviews a number of proposals in preprints dated 2004/5.
1867:"The landscape and the multiverse: What's the problem?"
1655:{\displaystyle P_{prior}\sim m_{soft}^{2n_{F}+n_{D}-1}}
1748:, are opposed to this use of the anthropic principle.
1695:
1668:
1573:
1450:
1406:
1379:
1326:
1306:
1265:
1146:
1123:
1094:
923:
896:
3224:
3201:
3178:
3125:
3010:
2918:
2860:
2792:
2741:
2708:
2603:
2560:
2450:frequently attacks the anthropic string landscape.
2149:Journal of Physics A: Mathematical and Theoretical
1799:; S. Ashok and M. Douglas, "Counting flux vacua",
1708:
1681:
1654:
1489:
1433:
1385:
1365:
1312:
1292:
1248:
1129:
1109:
942:
909:
2097:S. M. Carroll, "Is our universe natural?" (2005)
1069:Such attempts are based in the general ideas of
850:The term "landscape" comes from the notion of a
1784:, "The statistics of string / M theory vacua",
2308:Journal of Cosmology and Astroparticle Physics
2202:Journal of Cosmology and Astroparticle Physics
2538:
808:
8:
1562:Weak scale supersymmetry from the landscape
2545:
2531:
2523:
815:
801:
40:
29:
27:Collection of possible string theory vacua
2489:
2319:
2266:
2213:
2160:
2025:
1972:
1919:
1882:
1700:
1694:
1673:
1667:
1638:
1625:
1617:
1603:
1578:
1572:
1456:
1455:
1449:
1412:
1411:
1405:
1378:
1332:
1331:
1325:
1305:
1271:
1270:
1264:
1203:
1202:
1167:
1166:
1145:
1122:
1117:of observing some fundamental parameters
1093:
928:
922:
901:
895:
1865:Read, James; Le Bihan, Baptiste (2021).
1822:. Oxford University Press. p. 288.
1490:{\displaystyle P_{\mathrm {selection} }}
1366:{\displaystyle P_{\mathrm {selection} }}
1059:proposed that the observed value of the
858:. It was first applied to cosmology by
1842:L. Smolin, "Did the universe evolve?",
1773:
180:
154:
113:
79:
48:
32:
1004:Fine-tuning by the anthropic principle
1088:In such a framework, the probability
7:
2943:Bogomol'nyiâPrasadâSommerfield bound
1434:{\displaystyle P_{\mathrm {prior} }}
1293:{\displaystyle P_{\mathrm {prior} }}
258:= 4 supersymmetric YangâMills theory
2426:(Little, Brown, 2005). M. J. Rees,
1481:
1478:
1475:
1472:
1469:
1466:
1463:
1460:
1457:
1425:
1422:
1419:
1416:
1413:
1357:
1354:
1351:
1348:
1345:
1342:
1339:
1336:
1333:
1284:
1281:
1278:
1275:
1272:
1228:
1225:
1222:
1219:
1216:
1213:
1210:
1207:
1204:
1180:
1177:
1174:
1171:
1168:
890:is commonly thought to be roughly
189:Geometric Langlands correspondence
25:
1554:advocate it as a solution to the
876:Compactified CalabiâYau manifolds
1732:on the merits of the landscape.
839:) is the collection of possible
3140:Eleven-dimensional supergravity
886:In string theory the number of
1908:Journal of High Energy Physics
1240:
1234:
1192:
1186:
1156:
1150:
1104:
1098:
1:
2588:Second superstring revolution
2338:10.1088/1475-7516/2006/06/010
2232:10.1088/1475-7516/2006/05/009
2130:. See also the discussion at
1849:, 173â191 (1992). L. Smolin,
1844:Classical and Quantum Gravity
1556:cosmological constant problem
1539:Cosmological constant problem
3082:Generalized complex manifold
2583:First superstring revolution
943:{\displaystyle 10^{272,000}}
2179:10.1088/1751-8113/40/25/S22
973:. This is a version of the
954:and choices of generalized
3754:
2680:Non-critical string theory
2044:10.1103/PhysRevD.68.046005
1884:10.1007/s11229-021-03137-0
1048:
1007:
984:, was proposed in 2003 by
882:Compactification (physics)
879:
1991:10.1016/j.aop.2006.07.013
3216:Introduction to M-theory
2910:WessâZuminoâWitten model
2852:HananyâWitten transition
2578:History of string theory
2255:Prog. Theor. Phys. Suppl
910:{\displaystyle 10^{500}}
114:Non-perturbative results
2895:Vertex operator algebra
2595:String theory landscape
2478:Fortschritte der Physik
1938:10.1007/JHEP12(2015)164
1083:frequentist probability
833:string theory landscape
3193:AdS/CFT correspondence
2948:Exceptional Lie groups
2890:Superconformal algebra
2862:Conformal field theory
2733:MontonenâOlive duality
2685:Non-linear sigma model
2508:10.1002/prop.201000093
1852:The Life of the Cosmos
1730:SmolinâSusskind debate
1710:
1683:
1656:
1491:
1435:
1387:
1367:
1314:
1294:
1250:
1131:
1111:
1021:of constants like the
944:
911:
865:The Life of the Cosmos
230:Conformal field theory
147:AdS/CFT correspondence
3188:Holographic principle
3155:Type IIB supergravity
3150:Type IIA supergravity
3002:-form electrodynamics
2621:Bosonic string theory
1816:Baggott, Jim (2018).
1711:
1709:{\displaystyle n_{D}}
1684:
1682:{\displaystyle n_{F}}
1657:
1503:Simplified approaches
1492:
1436:
1388:
1368:
1315:
1295:
1251:
1132:
1112:
1061:cosmological constant
1023:cosmological constant
1010:Fine-tuning (physics)
945:
912:
273:Holographic principle
250:Twistor string theory
3107:HoĆavaâWitten theory
3054:HyperkÀhler manifold
2742:Particles and fields
2690:Tachyon condensation
2675:Matrix string theory
2285:10.1143/PTPS.163.245
1721:Scientific relevance
1693:
1666:
1571:
1448:
1404:
1377:
1324:
1304:
1263:
1144:
1121:
1110:{\displaystyle P(x)}
1092:
1071:Bayesian probability
1051:Bayesian probability
952:CalabiâYau manifolds
921:
894:
856:evolutionary biology
225:Theory of everything
18:Landscape multiverse
3145:Type I supergravity
3049:CalabiâYau manifold
3044:Ricci-flat manifold
3023:KaluzaâKlein theory
2764:RamondâRamond field
2670:String field theory
2500:2011ForPh..59..243C
2330:2006JCAP...06..010S
2277:2006PThPS.163..245G
2224:2006JCAP...05..009L
2171:2007JPhA...40.6777V
2036:2003PhRvD..68d6005K
1983:2007AnPhy.322.1096D
1930:2015JHEP...12..164T
1651:
1039:anthropic landscape
1035:anthropic principle
1014:Anthropic principle
263:KaluzaâKlein theory
199:Monstrous moonshine
80:Perturbative theory
49:Fundamental objects
3728:Physical cosmology
3112:K-theory (physics)
2989:ADE classification
2626:Superstring theory
1877:(3â4): 7749â7771.
1706:
1679:
1652:
1599:
1487:
1431:
1383:
1363:
1310:
1290:
1246:
1127:
1107:
1081:is problematic in
975:subset sum problem
940:
907:
837:landscape of vacua
3715:
3714:
3497:van Nieuwenhuizen
3033:Why 10 dimensions
2938:ChernâSimons form
2905:KacâMoody algebra
2885:Conformal algebra
2880:Conformal anomaly
2774:Magnetic monopole
2769:KalbâRamond field
2611:NambuâGoto action
2155:(25): 6777â6785.
2014:Physical Review D
1961:Annals of Physics
1829:978-0-19-253681-5
1736:Popular reception
1386:{\displaystyle x}
1313:{\displaystyle x}
1130:{\displaystyle x}
962:cycles, found in
852:fitness landscape
845:compactifications
825:
824:
556:van Nieuwenhuizen
16:(Redirected from
3745:
3225:String theorists
3165:Lie superalgebra
3117:Twisted K-theory
3075:Spin(7)-manifold
3028:Compactification
2870:Virasoro algebra
2653:Heterotic string
2547:
2540:
2533:
2524:
2519:
2493:
2484:(3â4): 243â283.
2451:
2444:
2438:
2420:
2414:
2396:
2390:
2377:Phys. Rev. Lett.
2373:
2367:
2356:
2350:
2349:
2323:
2303:
2297:
2296:
2270:
2250:
2244:
2243:
2217:
2215:astro-ph/0604242
2197:
2191:
2190:
2164:
2140:
2134:
2120:astro-ph/0511774
2112:
2106:
2095:
2089:
2083:Phys. Rev. Lett.
2079:
2073:
2062:
2056:
2055:
2029:
2009:
2003:
2002:
1976:
1967:(5): 1096â1142.
1956:
1950:
1949:
1923:
1903:
1897:
1896:
1886:
1862:
1856:
1840:
1834:
1833:
1813:
1807:
1778:
1763:Extra dimensions
1715:
1713:
1712:
1707:
1705:
1704:
1688:
1686:
1685:
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1677:
1661:
1659:
1658:
1653:
1650:
1643:
1642:
1630:
1629:
1616:
1595:
1594:
1552:Leonard Susskind
1496:
1494:
1493:
1488:
1486:
1485:
1484:
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1438:
1437:
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1430:
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1289:
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1255:
1253:
1252:
1247:
1233:
1232:
1231:
1185:
1184:
1183:
1136:
1134:
1133:
1128:
1116:
1114:
1113:
1108:
949:
947:
946:
941:
939:
938:
916:
914:
913:
908:
906:
905:
870:Leonard Susskind
817:
810:
803:
219:Related concepts
44:
30:
21:
3753:
3752:
3748:
3747:
3746:
3744:
3743:
3742:
3718:
3717:
3716:
3711:
3220:
3197:
3174:
3121:
3069:
3039:KĂ€hler manifold
3006:
2983:
2976:
2969:
2962:
2955:
2914:
2875:Mirror symmetry
2856:
2842:Brane cosmology
2788:
2737:
2704:
2660:N=2 superstring
2646:Type IIB string
2641:Type IIA string
2616:Polyakov action
2599:
2556:
2551:
2472:
2459:
2454:
2445:
2441:
2437:, 60â69 (2004).
2421:
2417:
2397:
2393:
2374:
2370:
2357:
2353:
2305:
2304:
2300:
2252:
2251:
2247:
2199:
2198:
2194:
2146:
2141:
2137:
2113:
2109:
2096:
2092:
2080:
2076:
2063:
2059:
2011:
2010:
2006:
1958:
1957:
1953:
1905:
1904:
1900:
1864:
1863:
1859:
1841:
1837:
1830:
1815:
1814:
1810:
1779:
1775:
1771:
1754:
1738:
1723:
1696:
1691:
1690:
1669:
1664:
1663:
1634:
1621:
1574:
1569:
1568:
1564:
1548:Sir Martin Rees
1541:
1533:
1505:
1451:
1446:
1445:
1407:
1402:
1401:
1375:
1374:
1327:
1322:
1321:
1302:
1301:
1266:
1261:
1260:
1198:
1162:
1142:
1141:
1119:
1118:
1090:
1089:
1057:Steven Weinberg
1053:
1047:
1016:
1008:Main articles:
1006:
956:magnetic fluxes
924:
919:
918:
917:, but could be
897:
892:
891:
884:
878:
821:
776:
775:
286:
278:
277:
235:Quantum gravity
220:
194:Mirror symmetry
28:
23:
22:
15:
12:
11:
5:
3751:
3749:
3741:
3740:
3735:
3730:
3720:
3719:
3713:
3712:
3710:
3709:
3704:
3699:
3694:
3689:
3684:
3679:
3674:
3669:
3664:
3659:
3654:
3649:
3644:
3639:
3634:
3629:
3624:
3619:
3614:
3609:
3604:
3599:
3594:
3589:
3584:
3579:
3574:
3569:
3564:
3559:
3554:
3549:
3547:Randjbar-Daemi
3544:
3539:
3534:
3529:
3524:
3519:
3514:
3509:
3504:
3499:
3494:
3489:
3484:
3479:
3474:
3469:
3464:
3459:
3454:
3449:
3444:
3439:
3434:
3429:
3424:
3419:
3414:
3409:
3404:
3399:
3394:
3389:
3384:
3379:
3374:
3369:
3364:
3359:
3354:
3349:
3344:
3339:
3334:
3329:
3324:
3319:
3314:
3309:
3304:
3299:
3294:
3289:
3284:
3279:
3274:
3269:
3264:
3259:
3254:
3249:
3244:
3239:
3234:
3228:
3226:
3222:
3221:
3219:
3218:
3213:
3207:
3205:
3199:
3198:
3196:
3195:
3190:
3184:
3182:
3176:
3175:
3173:
3172:
3170:Lie supergroup
3167:
3162:
3157:
3152:
3147:
3142:
3137:
3131:
3129:
3123:
3122:
3120:
3119:
3114:
3109:
3104:
3099:
3094:
3089:
3084:
3079:
3078:
3077:
3072:
3067:
3063:
3062:
3061:
3051:
3041:
3036:
3030:
3025:
3020:
3014:
3012:
3008:
3007:
3005:
3004:
2996:
2991:
2986:
2981:
2974:
2967:
2960:
2953:
2945:
2940:
2935:
2930:
2924:
2922:
2916:
2915:
2913:
2912:
2907:
2902:
2897:
2892:
2887:
2882:
2877:
2872:
2866:
2864:
2858:
2857:
2855:
2854:
2849:
2847:Quiver diagram
2844:
2839:
2834:
2829:
2824:
2819:
2814:
2809:
2804:
2798:
2796:
2790:
2789:
2787:
2786:
2781:
2776:
2771:
2766:
2761:
2756:
2751:
2745:
2743:
2739:
2738:
2736:
2735:
2730:
2725:
2720:
2714:
2712:
2710:String duality
2706:
2705:
2703:
2702:
2697:
2692:
2687:
2682:
2677:
2672:
2667:
2662:
2657:
2656:
2655:
2650:
2649:
2648:
2643:
2636:Type II string
2633:
2623:
2618:
2613:
2607:
2605:
2601:
2600:
2598:
2597:
2592:
2591:
2590:
2585:
2575:
2573:Cosmic strings
2570:
2564:
2562:
2558:
2557:
2552:
2550:
2549:
2542:
2535:
2527:
2521:
2520:
2474:CvetiÄ, Mirjam
2470:
2458:
2457:External links
2455:
2453:
2452:
2439:
2415:
2405:, 002 (2018),
2391:
2388:hep-ph/9801253
2382:, 1822 (1998).
2368:
2364:hep-th/0405279
2351:
2321:hep-th/0601162
2298:
2268:hep-th/0508005
2245:
2192:
2162:hep-th/0609193
2135:
2128:hep-ph/0512187
2107:
2103:hep-th/0512148
2090:
2088:, 2607 (1987).
2074:
2070:hep-th/0302219
2057:
2027:hep-th/0301240
2004:
1974:hep-th/0602072
1951:
1898:
1857:
1855:(Oxford, 1997)
1835:
1828:
1808:
1797:hep-th/0303194
1772:
1770:
1767:
1766:
1765:
1760:
1753:
1750:
1737:
1734:
1722:
1719:
1703:
1699:
1676:
1672:
1649:
1646:
1641:
1637:
1633:
1628:
1624:
1620:
1615:
1612:
1609:
1606:
1602:
1598:
1593:
1590:
1587:
1584:
1581:
1577:
1563:
1560:
1540:
1537:
1532:
1531:Interpretation
1529:
1504:
1501:
1500:
1499:
1483:
1480:
1477:
1474:
1471:
1468:
1465:
1462:
1459:
1454:
1442:
1427:
1424:
1421:
1418:
1415:
1410:
1400:The function
1382:
1359:
1356:
1353:
1350:
1347:
1344:
1341:
1338:
1335:
1330:
1309:
1286:
1283:
1280:
1277:
1274:
1269:
1257:
1256:
1245:
1242:
1239:
1236:
1230:
1227:
1224:
1221:
1218:
1215:
1212:
1209:
1206:
1201:
1197:
1194:
1191:
1188:
1182:
1179:
1176:
1173:
1170:
1165:
1161:
1158:
1155:
1152:
1149:
1126:
1106:
1103:
1100:
1097:
1049:Main article:
1046:
1045:Weinberg model
1043:
1005:
1002:
998:Sandip Trivedi
990:Renata Kallosh
982:KKLT mechanism
937:
934:
931:
927:
904:
900:
880:Main article:
877:
874:
823:
822:
820:
819:
812:
805:
797:
794:
793:
792:
791:
786:
778:
777:
774:
773:
768:
763:
758:
753:
748:
743:
738:
733:
728:
723:
718:
713:
708:
703:
698:
693:
688:
683:
678:
673:
668:
663:
658:
653:
648:
643:
638:
633:
628:
623:
618:
613:
608:
606:Randjbar-Daemi
603:
598:
593:
588:
583:
578:
573:
568:
563:
558:
553:
548:
543:
538:
533:
528:
523:
518:
513:
508:
503:
498:
493:
488:
483:
478:
473:
468:
463:
458:
453:
448:
443:
438:
433:
428:
423:
418:
413:
408:
403:
398:
393:
388:
383:
378:
373:
368:
363:
358:
353:
348:
343:
338:
333:
328:
323:
318:
313:
308:
303:
298:
293:
287:
284:
283:
280:
279:
276:
275:
270:
265:
260:
252:
247:
242:
237:
232:
227:
221:
218:
217:
214:
213:
212:
211:
206:
204:Vertex algebra
201:
196:
191:
183:
182:
178:
177:
176:
175:
170:
165:
157:
156:
152:
151:
150:
149:
144:
139:
134:
129:
124:
116:
115:
111:
110:
109:
108:
90:
82:
81:
77:
76:
75:
74:
69:
64:
59:
51:
50:
46:
45:
37:
36:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3750:
3739:
3736:
3734:
3733:String theory
3731:
3729:
3726:
3725:
3723:
3708:
3705:
3703:
3700:
3698:
3695:
3693:
3692:Zamolodchikov
3690:
3688:
3687:Zamolodchikov
3685:
3683:
3680:
3678:
3675:
3673:
3670:
3668:
3665:
3663:
3660:
3658:
3655:
3653:
3650:
3648:
3645:
3643:
3640:
3638:
3635:
3633:
3630:
3628:
3625:
3623:
3620:
3618:
3615:
3613:
3610:
3608:
3605:
3603:
3600:
3598:
3595:
3593:
3590:
3588:
3585:
3583:
3580:
3578:
3575:
3573:
3570:
3568:
3565:
3563:
3560:
3558:
3555:
3553:
3550:
3548:
3545:
3543:
3540:
3538:
3535:
3533:
3530:
3528:
3525:
3523:
3520:
3518:
3515:
3513:
3510:
3508:
3505:
3503:
3500:
3498:
3495:
3493:
3490:
3488:
3485:
3483:
3480:
3478:
3475:
3473:
3470:
3468:
3465:
3463:
3460:
3458:
3455:
3453:
3450:
3448:
3445:
3443:
3440:
3438:
3435:
3433:
3430:
3428:
3425:
3423:
3420:
3418:
3415:
3413:
3410:
3408:
3405:
3403:
3400:
3398:
3395:
3393:
3390:
3388:
3385:
3383:
3380:
3378:
3375:
3373:
3370:
3368:
3365:
3363:
3360:
3358:
3355:
3353:
3350:
3348:
3345:
3343:
3340:
3338:
3335:
3333:
3330:
3328:
3325:
3323:
3320:
3318:
3315:
3313:
3310:
3308:
3305:
3303:
3300:
3298:
3295:
3293:
3290:
3288:
3285:
3283:
3280:
3278:
3275:
3273:
3270:
3268:
3265:
3263:
3260:
3258:
3255:
3253:
3250:
3248:
3245:
3243:
3240:
3238:
3235:
3233:
3230:
3229:
3227:
3223:
3217:
3214:
3212:
3211:Matrix theory
3209:
3208:
3206:
3204:
3200:
3194:
3191:
3189:
3186:
3185:
3183:
3181:
3177:
3171:
3168:
3166:
3163:
3161:
3158:
3156:
3153:
3151:
3148:
3146:
3143:
3141:
3138:
3136:
3133:
3132:
3130:
3128:
3127:Supersymmetry
3124:
3118:
3115:
3113:
3110:
3108:
3105:
3103:
3100:
3098:
3095:
3093:
3090:
3088:
3085:
3083:
3080:
3076:
3073:
3071:
3064:
3060:
3057:
3056:
3055:
3052:
3050:
3047:
3046:
3045:
3042:
3040:
3037:
3034:
3031:
3029:
3026:
3024:
3021:
3019:
3016:
3015:
3013:
3009:
3003:
3001:
2997:
2995:
2992:
2990:
2987:
2984:
2977:
2970:
2963:
2956:
2949:
2946:
2944:
2941:
2939:
2936:
2934:
2931:
2929:
2926:
2925:
2923:
2921:
2917:
2911:
2908:
2906:
2903:
2901:
2898:
2896:
2893:
2891:
2888:
2886:
2883:
2881:
2878:
2876:
2873:
2871:
2868:
2867:
2865:
2863:
2859:
2853:
2850:
2848:
2845:
2843:
2840:
2838:
2835:
2833:
2830:
2828:
2825:
2823:
2820:
2818:
2815:
2813:
2810:
2808:
2805:
2803:
2800:
2799:
2797:
2795:
2791:
2785:
2782:
2780:
2779:Dual graviton
2777:
2775:
2772:
2770:
2767:
2765:
2762:
2760:
2757:
2755:
2752:
2750:
2747:
2746:
2744:
2740:
2734:
2731:
2729:
2726:
2724:
2721:
2719:
2716:
2715:
2713:
2711:
2707:
2701:
2698:
2696:
2695:RNS formalism
2693:
2691:
2688:
2686:
2683:
2681:
2678:
2676:
2673:
2671:
2668:
2666:
2663:
2661:
2658:
2654:
2651:
2647:
2644:
2642:
2639:
2638:
2637:
2634:
2632:
2631:Type I string
2629:
2628:
2627:
2624:
2622:
2619:
2617:
2614:
2612:
2609:
2608:
2606:
2602:
2596:
2593:
2589:
2586:
2584:
2581:
2580:
2579:
2576:
2574:
2571:
2569:
2566:
2565:
2563:
2559:
2555:
2554:String theory
2548:
2543:
2541:
2536:
2534:
2529:
2528:
2525:
2517:
2513:
2509:
2505:
2501:
2497:
2492:
2487:
2483:
2479:
2475:
2471:
2468:
2464:
2461:
2460:
2456:
2449:
2443:
2440:
2436:
2433:
2429:
2425:
2422:L. Susskind,
2419:
2416:
2412:
2408:
2404:
2401:
2395:
2392:
2389:
2385:
2381:
2378:
2372:
2369:
2365:
2361:
2355:
2352:
2347:
2343:
2339:
2335:
2331:
2327:
2322:
2317:
2313:
2309:
2302:
2299:
2294:
2290:
2286:
2282:
2278:
2274:
2269:
2264:
2260:
2256:
2249:
2246:
2241:
2237:
2233:
2229:
2225:
2221:
2216:
2211:
2207:
2203:
2196:
2193:
2188:
2184:
2180:
2176:
2172:
2168:
2163:
2158:
2154:
2150:
2145:
2139:
2136:
2132:
2129:
2125:
2121:
2117:
2111:
2108:
2104:
2100:
2094:
2091:
2087:
2084:
2078:
2075:
2071:
2067:
2061:
2058:
2053:
2049:
2045:
2041:
2037:
2033:
2028:
2023:
2020:(4): 046005.
2019:
2015:
2008:
2005:
2000:
1996:
1992:
1988:
1984:
1980:
1975:
1970:
1966:
1962:
1955:
1952:
1947:
1943:
1939:
1935:
1931:
1927:
1922:
1917:
1913:
1909:
1902:
1899:
1894:
1890:
1885:
1880:
1876:
1872:
1868:
1861:
1858:
1854:
1853:
1848:
1845:
1839:
1836:
1831:
1825:
1821:
1820:
1812:
1809:
1806:, 060 (2004).
1805:
1802:
1798:
1794:
1791:, 46 (2003).
1790:
1787:
1783:
1777:
1774:
1768:
1764:
1761:
1759:
1756:
1755:
1751:
1749:
1747:
1743:
1735:
1733:
1731:
1727:
1720:
1718:
1701:
1697:
1674:
1670:
1647:
1644:
1639:
1635:
1631:
1626:
1622:
1618:
1613:
1610:
1607:
1604:
1600:
1596:
1591:
1588:
1585:
1582:
1579:
1575:
1561:
1559:
1557:
1553:
1549:
1545:
1538:
1536:
1530:
1528:
1524:
1521:
1519:
1516:
1512:
1509:
1502:
1452:
1444:The function
1443:
1408:
1399:
1398:
1397:
1394:
1380:
1328:
1307:
1267:
1243:
1237:
1199:
1195:
1189:
1163:
1159:
1153:
1147:
1140:
1139:
1138:
1137:is given by,
1124:
1101:
1095:
1086:
1084:
1080:
1076:
1072:
1067:
1064:
1062:
1058:
1052:
1044:
1042:
1040:
1036:
1031:
1028:
1024:
1020:
1015:
1011:
1003:
1001:
999:
995:
991:
987:
986:Shamit Kachru
983:
978:
976:
972:
967:
965:
961:
958:over various
957:
953:
935:
932:
929:
925:
902:
898:
889:
883:
875:
873:
871:
867:
866:
861:
857:
853:
848:
846:
842:
838:
834:
830:
829:string theory
818:
813:
811:
806:
804:
799:
798:
796:
795:
790:
787:
785:
782:
781:
780:
779:
772:
769:
767:
764:
762:
759:
757:
756:Zamolodchikov
754:
752:
751:Zamolodchikov
749:
747:
744:
742:
739:
737:
734:
732:
729:
727:
724:
722:
719:
717:
714:
712:
709:
707:
704:
702:
699:
697:
694:
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34:String theory
31:
19:
3237:Arkani-Hamed
3135:Supergravity
3102:Moduli space
2999:
2994:Dirac string
2920:Gauge theory
2900:Loop algebra
2837:Black string
2700:GS formalism
2594:
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2017:
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1395:
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1087:
1079:distribution
1068:
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1038:
1032:
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994:Andrei Linde
981:
979:
968:
885:
863:
862:in his book
849:
836:
832:
826:
296:Arkani-Hamed
255:
245:Supergravity
172:
3597:Silverstein
3097:Orientifold
2832:Black holes
2827:Black brane
2784:Dual photon
1914:(12): 164.
1726:David Gross
1518:dark matter
1027:Higgs boson
1019:Fine-tuning
971:NP complete
841:false vacua
656:Silverstein
181:Mathematics
93:Superstring
3738:Multiverse
3722:Categories
3617:Strominger
3612:Steinhardt
3607:Staudacher
3522:Polchinski
3472:Nanopoulos
3432:Mandelstam
3412:Kontsevich
3252:Berenstein
3180:Holography
3160:Superspace
3059:K3 surface
3018:Worldsheet
2933:Instantons
2561:Background
2411:1712.01399
2314:(6): 010.
2261:: 245â57.
2208:(5): 009.
1921:1511.03209
1782:M. Douglas
1769:References
1746:Peter Woit
1742:Lubos Motl
888:flux vacua
860:Lee Smolin
676:Strominger
671:Steinhardt
666:Staudacher
581:Polchinski
531:Nanopoulos
491:Mandelstam
471:Kontsevich
311:Berenstein
268:Multiverse
3652:Veneziano
3532:Rajaraman
3427:Maldacena
3317:Gopakumar
3267:Dijkgraaf
3262:Curtright
2928:Anomalies
2807:NS5-brane
2728:U-duality
2723:S-duality
2718:T-duality
2491:1009.5386
2467:arxiv.org
2346:119337679
2293:118936307
2187:119390736
2052:119482182
1893:234815857
1758:Swampland
1645:−
1597:∼
1498:universe.
1196:×
1055:In 1987,
716:Veneziano
591:Rajaraman
486:Maldacena
376:Gopakumar
326:Dijkgraaf
321:Curtright
285:Theorists
173:Landscape
168:Cosmology
132:U-duality
127:T-duality
122:S-duality
105:Heterotic
3707:Zwiebach
3662:Verlinde
3657:Verlinde
3632:Townsend
3627:Susskind
3562:Sagnotti
3527:Polyakov
3482:Nekrasov
3447:Minwalla
3442:Martinec
3407:Knizhnik
3402:Klebanov
3397:Kapustin
3362:'t Hooft
3297:Fischler
3232:AganagiÄ
3203:M-theory
3092:Conifold
3087:Orbifold
3070:manifold
3011:Geometry
2817:M5-brane
2812:M2-brane
2749:Graviton
2665:F-theory
2516:46634583
2432:Sci. Am.
2240:39340203
1946:41149049
1871:Synthese
1752:See also
964:F-theory
960:homology
789:Glossary
771:Zwiebach
726:Verlinde
721:Verlinde
696:Townsend
691:'t Hooft
686:Susskind
621:Sagnotti
586:Polyakov
541:Nekrasov
506:Minwalla
501:Martinec
466:Knizhnik
461:Klebanov
456:Kapustin
426:Horowitz
356:Fischler
291:AganagiÄ
209:K-theory
142:F-theory
137:M-theory
3637:Trivedi
3622:Sundrum
3587:Shenker
3577:Seiberg
3572:Schwarz
3542:Randall
3502:Novikov
3492:Nielsen
3477:NÄstase
3387:Kallosh
3372:Gibbons
3312:Gliozzi
3302:Friedan
3292:Ferrara
3277:Douglas
3272:Distler
2822:S-brane
2802:D-brane
2759:Tachyon
2754:Dilaton
2568:Strings
2496:Bibcode
2326:Bibcode
2273:Bibcode
2220:Bibcode
2167:Bibcode
2032:Bibcode
1979:Bibcode
1926:Bibcode
1508:Tegmark
1077:from a
1025:or the
784:History
701:Trivedi
681:Sundrum
646:Shenker
636:Seiberg
631:Schwarz
601:Randall
561:Novikov
551:Nielsen
536:NÄstase
446:Kallosh
431:Gibbons
371:Gliozzi
361:Friedan
351:Ferrara
336:Douglas
331:Distler
101:Type II
88:Bosonic
72:D-brane
3702:Zumino
3697:Zaslow
3682:Yoneya
3672:Witten
3592:Siegel
3567:Scherk
3537:Ramond
3512:Ooguri
3437:Marolf
3392:Kaluza
3377:Kachru
3367:HoĆava
3357:Harvey
3352:Hanson
3337:Gubser
3327:Greene
3257:Bousso
3242:Atiyah
2794:Branes
2604:Theory
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2344:
2291:
2238:
2185:
2050:
1999:281586
1997:
1944:
1891:
1826:
1662:where
1511:et al.
1259:where
1075:sample
996:, and
831:, the
766:Zumino
761:Zaslow
746:Yoneya
736:Witten
651:Siegel
626:Scherk
596:Ramond
571:Ooguri
496:Marolf
451:Kaluza
436:Kachru
421:HoĆava
416:Harvey
411:Hanson
396:Gubser
386:Greene
316:Bousso
301:Atiyah
97:Type I
57:String
3642:Turok
3552:RoÄek
3517:Ovrut
3507:Olive
3487:Neveu
3467:Myers
3462:Mukhi
3452:Moore
3422:Linde
3417:Klein
3342:Gukov
3332:Gross
3322:Green
3307:Gates
3287:Dvali
3247:Banks
2512:S2CID
2486:arXiv
2407:arXiv
2384:arXiv
2360:arXiv
2342:S2CID
2316:arXiv
2289:S2CID
2263:arXiv
2236:S2CID
2210:arXiv
2183:S2CID
2157:arXiv
2142:See,
2124:arXiv
2116:arXiv
2099:arXiv
2066:arXiv
2048:S2CID
2022:arXiv
1995:S2CID
1969:arXiv
1942:S2CID
1916:arXiv
1889:S2CID
1793:arXiv
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706:Turok
611:RoÄek
576:Ovrut
566:Olive
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511:Moore
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381:Green
366:Gates
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3457:Motl
3382:Kaku
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2448:blog
2400:JHEP
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2206:0605
2144:e.g.
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