979:
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49:
1244:
states that the derived category of coherent sheaves on one CalabiâYau manifold is equivalent in a certain sense to the Fukaya category of a completely different CalabiâYau manifold. This equivalence provides an unexpected bridge between two branches of geometry, namely complex and symplectic
1181:
at the endpoints of strings. Intuitively, one can think of a submanifold as a surface embedded inside of a CalabiâYau manifold, although submanifolds can also exist in dimensions different from two. In mathematical language, the category having these branes as its objects is known as the
1198:. This means, among other things, that they have half the dimension of the space in which they sit, and they are length-, area-, or volume-minimizing. The category having these branes as its objects is called the
1001:
are an important class of branes that arise when one considers open strings. As an open string propagates through spacetime, its endpoints are required to lie on a D-brane. The letter "D" in D-brane refers to the
2153:
Aspinwall, Paul; Bridgeland, Tom; Craw, Alastair; Douglas, Michael; Gross, Mark; Kapustin, Anton; Moore, Gregory; Segal, Graeme; Szendröi, Balåzs; Wilson, P.M.H., eds. (2009).
2693:
1129:
1085:
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1105:
2295:
261:
1029:, a theoretical tool that physicists use to translate difficult problems in gauge theory into more mathematically tractable problems in string theory.
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between these structures. One can likewise consider categories where the objects are D-branes and the morphisms between two branes
1194:, the D-branes can again be viewed as submanifolds of a CalabiâYau manifold. Roughly speaking, they are what mathematicians call
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1013:, a kind of highly symmetric physical theory which is also used to describe the behavior of elementary particles in the
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One crucial point about D-branes is that the dynamics on the D-brane worldvolume is described by a
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The Shape of Inner Space: String Theory and the
Geometry of the Universe's Hidden Dimensions
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may be open (forming a segment with two endpoints) or closed (forming a closed loop).
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A point particle is a 0-brane, of dimension zero; a string, named after vibrating
2203:
1980:
1922:
1051:
between them. In most examples, the objects are mathematical structures (such as
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857:, or a two-dimensional membrane to higher-dimensional objects. Branes are
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2842:
2837:
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2499:
2415:
1780:
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1508:
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The derived category of coherent sheaves is constructed using tools from
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148:
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17:
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78:
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1622:
1606:
1500:
1478:
2253:
Zaslow, Eric (2008). "Mirror
Symmetry". In Gowers, Timothy (ed.).
1610:
1520:
1190:
on the CalabiâYau. In another version of string theory called the
1177:, together with additional data that arise physically from having
1153:
977:
2273:
1772:
1504:
1230:
926:, is a 2-brane. The corresponding object of arbitrary dimension
870:
2277:
1602:
1217:. On the other hand, the Fukaya category is constructed using
1037:
Mathematically, branes can be described using the notion of a
1209:, a branch of mathematics that describes geometric shapes in
846:
is a physical object that generalizes the notion of a zero-
899:
The word "brane" originated in 1987 as a contraction of "
2041:
A basic reference on category theory is Mac Lane 1998.
1989:, "Semiclassical quantization of the supermembrane",
1225:. Symplectic geometry studies spaces equipped with a
1221:, a branch of mathematics that arose from studies of
1137:
1117:
1093:
1073:
1017:. This connection has led to important insights into
2975:
2952:
2929:
2876:
2761:
2669:
2611:
2543:
2492:
2459:
2354:
2311:
1921:
1229:, a mathematical tool that can be used to compute
1143:
1123:
1099:
1079:
1041:. This is a mathematical structure consisting of
880:Mathematically, branes can be represented within
952:+1)-dimensional volume in spacetime called its
1025:. For example, it led to the discovery of the
2289:
1165:In one version of string theory known as the
815:
8:
964:, which live on the worldvolume of a brane.
2296:
2282:
2274:
822:
808:
47:
36:
1173:of certain six-dimensional shapes called
1136:
1116:
1092:
1072:
27:Extended physical object in string theory
2182:Categories for the Working Mathematician
1289:
1045:, and for any pair of objects, a set of
918:, is a 1-brane; a membrane, named after
1913:
187:
161:
120:
86:
55:
39:
2256:The Princeton Companion to Mathematics
2230:Yau, Shing-Tung; Nadis, Steve (2010).
1458:Atomic, molecular, and optical physics
873:and can have other attributes such as
1712:Newton's law of universal gravitation
7:
2694:Bogomol'nyiâPrasadâSommerfield bound
2155:Dirichlet Branes and Mirror Symmetry
1942:participating institution membership
1213:and solves geometric problems using
861:objects which can propagate through
265:= 4 supersymmetric YangâMills theory
982:Open strings attached to a pair of
1111:of open strings stretched between
1015:standard model of particle physics
196:Geometric Langlands correspondence
25:
1471:Atomic and molecular astrophysics
1561:Nanoscale and mesoscopic physics
2891:Eleven-dimensional supergravity
1196:special Lagrangian submanifolds
1006:, which the D-brane satisfies.
1333:Particle physics phenomenology
838:and related theories (such as
1:
2339:Second superstring revolution
2163:American Mathematical Society
2131:Aspinwall et al. 2009, p. 616
2113:Yau and Nadis 2010, pp. 180â1
1423:Spontaneous symmetry breaking
1233:in two-dimensional examples.
2833:Generalized complex manifold
2334:First superstring revolution
2159:Clay Mathematics Monographs
2147:General and cited references
2104:Aspinwal et al. 2009, p. 575
2086:Aspinwal et al. 2009, p. 575
2077:Aspinwal et al. 2009, p. 575
1004:Dirichlet boundary condition
2204:"What is ... a Brane?"
2180:Mac Lane, Saunders (1998).
1897:Quantum information science
1729:Cosmic background radiation
1496:Quantum information science
1238:homological mirror symmetry
890:homological mirror symmetry
3495:
2431:Non-critical string theory
2140:Yau and Nadis 2010, p. 181
2095:Yau and Nadis 2010, p. 175
2068:Yau and Nadis 2010, p. 165
971:
865:according to the rules of
29:
1929:Oxford English Dictionary
1791:
1761:Gravitational singularity
1578:Density functional theory
1517:Electromagnetic radiation
956:. Physicists often study
934:-brane, a term coined by
2967:Introduction to M-theory
2661:WessâZuminoâWitten model
2603:HananyâWitten transition
2329:History of string theory
1675:High-energy astrophysics
1615:BoseâEinstein condensate
1540:Condensed matter physics
1063:) and the morphisms are
121:Non-perturbative results
2646:Vertex operator algebra
2346:String theory landscape
1934:Oxford University Press
1757:Gravitational radiation
1553:Low-temperature physics
1391:Fundamental interaction
1346:Quantum electrodynamics
1124:{\displaystyle \alpha }
1080:{\displaystyle \alpha }
1033:Categorical description
894:noncommutative geometry
2944:AdS/CFT correspondence
2699:Exceptional Lie groups
2641:Superconformal algebra
2613:Conformal field theory
2484:MontonenâOlive duality
2436:Non-linear sigma model
1877:Physics of computation
1679:Planetary astrophysics
1386:AdS/CFT correspondence
1358:Effective field theory
1350:Quantum chromodynamics
1270:Lagrangian submanifold
1162:
1145:
1144:{\displaystyle \beta }
1125:
1101:
1100:{\displaystyle \beta }
1081:
1027:AdS/CFT correspondence
986:
237:Conformal field theory
154:AdS/CFT correspondence
32:Brane (disambiguation)
2939:Holographic principle
2906:Type IIB supergravity
2901:Type IIA supergravity
2753:-form electrodynamics
2372:Bosonic string theory
2032:Aspinwall et al. 2009
1873:Physical oceanography
1817:Communication physics
1619:Electrical conduction
1594:Statistical mechanics
1549:High-pressure physics
1329:Astroparticle physics
1158:A cross section of a
1157:
1146:
1126:
1102:
1082:
981:
962:electromagnetic field
948:-brane sweeps out a (
884:, and are studied in
840:supergravity theories
280:Holographic principle
257:Twistor string theory
2858:HoĆavaâWitten theory
2805:HyperkÀhler manifold
2493:Particles and fields
2441:Tachyon condensation
2426:Matrix string theory
1720:Magnetohydrodynamics
1695:Stellar astrophysics
1525:Polarization (waves)
1447:Theory of everything
1427:Neutrino oscillation
1374:Grand Unified Theory
1362:Lattice field theory
1342:Quantum field theory
1321:Nuclear astrophysics
1175:CalabiâYau manifolds
1171:complex submanifolds
1135:
1115:
1091:
1071:
1023:quantum field theory
853:, a one-dimensional
232:Theory of everything
30:For other uses, see
2896:Type I supergravity
2800:CalabiâYau manifold
2795:Ricci-flat manifold
2774:KaluzaâKlein theory
2515:RamondâRamond field
2421:String field theory
2122:Zaslow 2008, p. 531
2059:Zaslow 2008, p. 536
2050:Zaslow 2008, p. 536
1932:(Online ed.).
1893:Quantum electronics
1885:Solid-state devices
1825:Engineering physics
1805:Atmospheric physics
1793:Accelerator physics
1671:Gravitation physics
1586:Fermi liquid theory
1545:Solid-state physics
1411:Elementary particle
1219:symplectic geometry
1215:algebraic equations
1192:topological A-model
1169:, the D-branes are
1167:topological B-model
1160:CalabiâYau manifold
920:vibrating membranes
270:KaluzaâKlein theory
206:Monstrous moonshine
87:Perturbative theory
56:Fundamental objects
2863:K-theory (physics)
2740:ADE classification
2377:Superstring theory
2211:Notices of the AMS
2023:Moore 2005, p. 215
2014:Moore 2005, p. 215
2005:Moore 2005, p. 214
1954:Moore 2005, p. 214
1869:Physical chemistry
1708:General relativity
1378:Superstring theory
1354:Electroweak theory
1163:
1141:
1121:
1097:
1077:
1061:topological spaces
987:
3466:
3465:
3248:van Nieuwenhuizen
2784:Why 10 dimensions
2689:ChernâSimons form
2656:KacâMoody algebra
2636:Conformal algebra
2631:Conformal anomaly
2525:Magnetic monopole
2520:KalbâRamond field
2362:NambuâGoto action
2266:978-0-691-11880-2
2245:978-0-465-02023-2
2191:978-0-387-98403-2
2172:978-0-8218-3848-8
1940:(Subscription or
1906:
1905:
1889:Quantum chemistry
1841:Materials physics
1631:Self-organization
1492:Quantum chemistry
1467:Molecular physics
1223:classical physics
960:analogous to the
888:for insight into
867:quantum mechanics
832:
831:
563:van Nieuwenhuizen
16:(Redirected from
3486:
2976:String theorists
2916:Lie superalgebra
2868:Twisted K-theory
2826:Spin(7)-manifold
2779:Compactification
2621:Virasoro algebra
2404:Heterotic string
2298:
2291:
2284:
2275:
2270:
2249:
2226:
2224:
2222:
2208:
2195:
2176:
2141:
2138:
2132:
2129:
2123:
2120:
2114:
2111:
2105:
2102:
2096:
2093:
2087:
2084:
2078:
2075:
2069:
2066:
2060:
2057:
2051:
2048:
2042:
2039:
2033:
2030:
2024:
2021:
2015:
2012:
2006:
2003:
1997:
1984:
1961:
1955:
1952:
1946:
1945:
1937:
1925:
1918:
1901:Vehicle dynamics
1813:Chemical physics
1716:Lambda-CDM model
1704:Cosmic inflation
1590:Many-body theory
1475:Chemical physics
1431:Seesaw mechanism
1325:Particle physics
1312:particle physics
1290:
1242:Maxim Kontsevich
1207:complex geometry
1188:coherent sheaves
1184:derived category
1150:
1148:
1147:
1142:
1130:
1128:
1127:
1122:
1106:
1104:
1103:
1098:
1086:
1084:
1083:
1078:
886:pure mathematics
824:
817:
810:
226:Related concepts
51:
37:
21:
3494:
3493:
3489:
3488:
3487:
3485:
3484:
3483:
3469:
3468:
3467:
3462:
2971:
2948:
2925:
2872:
2820:
2790:KĂ€hler manifold
2757:
2734:
2727:
2720:
2713:
2706:
2665:
2626:Mirror symmetry
2607:
2593:Brane cosmology
2539:
2488:
2455:
2411:N=2 superstring
2397:Type IIB string
2392:Type IIA string
2367:Polyakov action
2350:
2307:
2302:
2267:
2252:
2246:
2229:
2220:
2218:
2206:
2198:
2192:
2179:
2173:
2161:. Vol. 4.
2152:
2149:
2144:
2139:
2135:
2130:
2126:
2121:
2117:
2112:
2108:
2103:
2099:
2094:
2090:
2085:
2081:
2076:
2072:
2067:
2063:
2058:
2054:
2049:
2045:
2040:
2036:
2031:
2027:
2022:
2018:
2013:
2009:
2004:
2000:
1978:
1962:
1958:
1953:
1949:
1939:
1920:
1919:
1915:
1911:
1857:Optoelectronics
1845:Medical physics
1788:Applied physics
1574:Bloch's theorem
1565:Polymer physics
1557:Surface physics
1443:Quantum gravity
1399:electromagnetic
1317:Nuclear physics
1260:Brane cosmology
1251:
1227:symplectic form
1211:algebraic terms
1200:Fukaya category
1133:
1132:
1113:
1112:
1089:
1088:
1069:
1068:
1035:
976:
970:
916:musical strings
912:
828:
783:
782:
293:
285:
284:
242:Quantum gravity
227:
201:Mirror symmetry
35:
28:
23:
22:
15:
12:
11:
5:
3492:
3490:
3482:
3481:
3471:
3470:
3464:
3463:
3461:
3460:
3455:
3450:
3445:
3440:
3435:
3430:
3425:
3420:
3415:
3410:
3405:
3400:
3395:
3390:
3385:
3380:
3375:
3370:
3365:
3360:
3355:
3350:
3345:
3340:
3335:
3330:
3325:
3320:
3315:
3310:
3305:
3300:
3298:Randjbar-Daemi
3295:
3290:
3285:
3280:
3275:
3270:
3265:
3260:
3255:
3250:
3245:
3240:
3235:
3230:
3225:
3220:
3215:
3210:
3205:
3200:
3195:
3190:
3185:
3180:
3175:
3170:
3165:
3160:
3155:
3150:
3145:
3140:
3135:
3130:
3125:
3120:
3115:
3110:
3105:
3100:
3095:
3090:
3085:
3080:
3075:
3070:
3065:
3060:
3055:
3050:
3045:
3040:
3035:
3030:
3025:
3020:
3015:
3010:
3005:
3000:
2995:
2990:
2985:
2979:
2977:
2973:
2972:
2970:
2969:
2964:
2958:
2956:
2950:
2949:
2947:
2946:
2941:
2935:
2933:
2927:
2926:
2924:
2923:
2921:Lie supergroup
2918:
2913:
2908:
2903:
2898:
2893:
2888:
2882:
2880:
2874:
2873:
2871:
2870:
2865:
2860:
2855:
2850:
2845:
2840:
2835:
2830:
2829:
2828:
2823:
2818:
2814:
2813:
2812:
2802:
2792:
2787:
2781:
2776:
2771:
2765:
2763:
2759:
2758:
2756:
2755:
2747:
2742:
2737:
2732:
2725:
2718:
2711:
2704:
2696:
2691:
2686:
2681:
2675:
2673:
2667:
2666:
2664:
2663:
2658:
2653:
2648:
2643:
2638:
2633:
2628:
2623:
2617:
2615:
2609:
2608:
2606:
2605:
2600:
2598:Quiver diagram
2595:
2590:
2585:
2580:
2575:
2570:
2565:
2560:
2555:
2549:
2547:
2541:
2540:
2538:
2537:
2532:
2527:
2522:
2517:
2512:
2507:
2502:
2496:
2494:
2490:
2489:
2487:
2486:
2481:
2476:
2471:
2465:
2463:
2461:String duality
2457:
2456:
2454:
2453:
2448:
2443:
2438:
2433:
2428:
2423:
2418:
2413:
2408:
2407:
2406:
2401:
2400:
2399:
2394:
2387:Type II string
2384:
2374:
2369:
2364:
2358:
2356:
2352:
2351:
2349:
2348:
2343:
2342:
2341:
2336:
2326:
2324:Cosmic strings
2321:
2315:
2313:
2309:
2308:
2303:
2301:
2300:
2293:
2286:
2278:
2272:
2271:
2265:
2250:
2244:
2227:
2200:Moore, Gregory
2196:
2190:
2177:
2171:
2148:
2145:
2143:
2142:
2133:
2124:
2115:
2106:
2097:
2088:
2079:
2070:
2061:
2052:
2043:
2034:
2025:
2016:
2007:
1998:
1956:
1947:
1912:
1910:
1907:
1904:
1903:
1881:Plasma physics
1849:Nanotechnology
1829:Fluid dynamics
1790:
1784:
1783:
1722:
1697:
1683:Plasma physics
1656:
1650:
1649:
1639:superconductor
1596:
1567:
1542:
1536:
1535:
1533:Casimir effect
1498:
1488:Quantum optics
1485:
1463:Atomic physics
1460:
1454:
1453:
1388:
1338:Standard Model
1335:
1314:
1304:
1303:
1300:
1299:Major theories
1297:
1294:
1288:
1287:
1282:
1277:
1272:
1267:
1265:Dirac membrane
1262:
1257:
1250:
1247:
1240:conjecture of
1140:
1120:
1096:
1076:
1034:
1031:
972:Main article:
969:
966:
911:
905:
851:point particle
830:
829:
827:
826:
819:
812:
804:
801:
800:
799:
798:
793:
785:
784:
781:
780:
775:
770:
765:
760:
755:
750:
745:
740:
735:
730:
725:
720:
715:
710:
705:
700:
695:
690:
685:
680:
675:
670:
665:
660:
655:
650:
645:
640:
635:
630:
625:
620:
615:
613:Randjbar-Daemi
610:
605:
600:
595:
590:
585:
580:
575:
570:
565:
560:
555:
550:
545:
540:
535:
530:
525:
520:
515:
510:
505:
500:
495:
490:
485:
480:
475:
470:
465:
460:
455:
450:
445:
440:
435:
430:
425:
420:
415:
410:
405:
400:
395:
390:
385:
380:
375:
370:
365:
360:
355:
350:
345:
340:
335:
330:
325:
320:
315:
310:
305:
300:
294:
291:
290:
287:
286:
283:
282:
277:
272:
267:
259:
254:
249:
244:
239:
234:
228:
225:
224:
221:
220:
219:
218:
213:
211:Vertex algebra
208:
203:
198:
190:
189:
185:
184:
183:
182:
177:
172:
164:
163:
159:
158:
157:
156:
151:
146:
141:
136:
131:
123:
122:
118:
117:
116:
115:
97:
89:
88:
84:
83:
82:
81:
76:
71:
66:
58:
57:
53:
52:
44:
43:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3491:
3480:
3479:String theory
3477:
3476:
3474:
3459:
3456:
3454:
3451:
3449:
3446:
3444:
3443:Zamolodchikov
3441:
3439:
3438:Zamolodchikov
3436:
3434:
3431:
3429:
3426:
3424:
3421:
3419:
3416:
3414:
3411:
3409:
3406:
3404:
3401:
3399:
3396:
3394:
3391:
3389:
3386:
3384:
3381:
3379:
3376:
3374:
3371:
3369:
3366:
3364:
3361:
3359:
3356:
3354:
3351:
3349:
3346:
3344:
3341:
3339:
3336:
3334:
3331:
3329:
3326:
3324:
3321:
3319:
3316:
3314:
3311:
3309:
3306:
3304:
3301:
3299:
3296:
3294:
3291:
3289:
3286:
3284:
3281:
3279:
3276:
3274:
3271:
3269:
3266:
3264:
3261:
3259:
3256:
3254:
3251:
3249:
3246:
3244:
3241:
3239:
3236:
3234:
3231:
3229:
3226:
3224:
3221:
3219:
3216:
3214:
3211:
3209:
3206:
3204:
3201:
3199:
3196:
3194:
3191:
3189:
3186:
3184:
3181:
3179:
3176:
3174:
3171:
3169:
3166:
3164:
3161:
3159:
3156:
3154:
3151:
3149:
3146:
3144:
3141:
3139:
3136:
3134:
3131:
3129:
3126:
3124:
3121:
3119:
3116:
3114:
3111:
3109:
3106:
3104:
3101:
3099:
3096:
3094:
3091:
3089:
3086:
3084:
3081:
3079:
3076:
3074:
3071:
3069:
3066:
3064:
3061:
3059:
3056:
3054:
3051:
3049:
3046:
3044:
3041:
3039:
3036:
3034:
3031:
3029:
3026:
3024:
3021:
3019:
3016:
3014:
3011:
3009:
3006:
3004:
3001:
2999:
2996:
2994:
2991:
2989:
2986:
2984:
2981:
2980:
2978:
2974:
2968:
2965:
2963:
2962:Matrix theory
2960:
2959:
2957:
2955:
2951:
2945:
2942:
2940:
2937:
2936:
2934:
2932:
2928:
2922:
2919:
2917:
2914:
2912:
2909:
2907:
2904:
2902:
2899:
2897:
2894:
2892:
2889:
2887:
2884:
2883:
2881:
2879:
2878:Supersymmetry
2875:
2869:
2866:
2864:
2861:
2859:
2856:
2854:
2851:
2849:
2846:
2844:
2841:
2839:
2836:
2834:
2831:
2827:
2824:
2822:
2815:
2811:
2808:
2807:
2806:
2803:
2801:
2798:
2797:
2796:
2793:
2791:
2788:
2785:
2782:
2780:
2777:
2775:
2772:
2770:
2767:
2766:
2764:
2760:
2754:
2752:
2748:
2746:
2743:
2741:
2738:
2735:
2728:
2721:
2714:
2707:
2700:
2697:
2695:
2692:
2690:
2687:
2685:
2682:
2680:
2677:
2676:
2674:
2672:
2668:
2662:
2659:
2657:
2654:
2652:
2649:
2647:
2644:
2642:
2639:
2637:
2634:
2632:
2629:
2627:
2624:
2622:
2619:
2618:
2616:
2614:
2610:
2604:
2601:
2599:
2596:
2594:
2591:
2589:
2586:
2584:
2581:
2579:
2576:
2574:
2571:
2569:
2566:
2564:
2561:
2559:
2556:
2554:
2551:
2550:
2548:
2546:
2542:
2536:
2533:
2531:
2530:Dual graviton
2528:
2526:
2523:
2521:
2518:
2516:
2513:
2511:
2508:
2506:
2503:
2501:
2498:
2497:
2495:
2491:
2485:
2482:
2480:
2477:
2475:
2472:
2470:
2467:
2466:
2464:
2462:
2458:
2452:
2449:
2447:
2446:RNS formalism
2444:
2442:
2439:
2437:
2434:
2432:
2429:
2427:
2424:
2422:
2419:
2417:
2414:
2412:
2409:
2405:
2402:
2398:
2395:
2393:
2390:
2389:
2388:
2385:
2383:
2382:Type I string
2380:
2379:
2378:
2375:
2373:
2370:
2368:
2365:
2363:
2360:
2359:
2357:
2353:
2347:
2344:
2340:
2337:
2335:
2332:
2331:
2330:
2327:
2325:
2322:
2320:
2317:
2316:
2314:
2310:
2306:
2305:String theory
2299:
2294:
2292:
2287:
2285:
2280:
2279:
2276:
2268:
2262:
2258:
2257:
2251:
2247:
2241:
2237:
2233:
2228:
2216:
2212:
2205:
2201:
2197:
2193:
2187:
2183:
2178:
2174:
2168:
2164:
2160:
2156:
2151:
2150:
2146:
2137:
2134:
2128:
2125:
2119:
2116:
2110:
2107:
2101:
2098:
2092:
2089:
2083:
2080:
2074:
2071:
2065:
2062:
2056:
2053:
2047:
2044:
2038:
2035:
2029:
2026:
2020:
2017:
2011:
2008:
2002:
1999:
1995:
1992:
1988:
1982:
1977:
1973:
1969:
1965:
1960:
1957:
1951:
1948:
1943:
1935:
1931:
1930:
1924:
1917:
1914:
1908:
1902:
1898:
1894:
1890:
1886:
1882:
1878:
1874:
1870:
1866:
1865:Photovoltaics
1862:
1858:
1854:
1850:
1846:
1842:
1838:
1837:Laser physics
1834:
1830:
1826:
1822:
1818:
1814:
1810:
1806:
1802:
1798:
1794:
1789:
1786:
1785:
1782:
1778:
1774:
1770:
1766:
1762:
1758:
1754:
1750:
1746:
1742:
1738:
1734:
1733:Cosmic string
1730:
1726:
1723:
1721:
1717:
1713:
1709:
1705:
1701:
1698:
1696:
1692:
1691:Space physics
1688:
1687:Solar physics
1684:
1680:
1676:
1672:
1668:
1664:
1660:
1657:
1655:
1652:
1651:
1648:
1644:
1643:superfluidity
1640:
1636:
1635:Semiconductor
1632:
1628:
1624:
1620:
1616:
1612:
1608:
1604:
1600:
1597:
1595:
1591:
1587:
1583:
1579:
1575:
1571:
1568:
1566:
1562:
1558:
1554:
1550:
1546:
1543:
1541:
1538:
1537:
1534:
1530:
1529:Spectral line
1526:
1522:
1518:
1514:
1510:
1506:
1502:
1499:
1497:
1493:
1489:
1486:
1484:
1480:
1476:
1472:
1468:
1464:
1461:
1459:
1456:
1455:
1452:
1451:Vacuum energy
1448:
1444:
1440:
1436:
1432:
1428:
1424:
1420:
1416:
1412:
1408:
1404:
1400:
1396:
1395:gravitational
1392:
1389:
1387:
1383:
1379:
1375:
1371:
1370:Supersymmetry
1367:
1363:
1359:
1355:
1351:
1347:
1343:
1339:
1336:
1334:
1330:
1326:
1322:
1318:
1315:
1313:
1309:
1306:
1305:
1301:
1298:
1295:
1292:
1291:
1286:
1283:
1281:
1278:
1276:
1273:
1271:
1268:
1266:
1263:
1261:
1258:
1256:
1253:
1252:
1248:
1246:
1243:
1239:
1234:
1232:
1228:
1224:
1220:
1216:
1212:
1208:
1203:
1201:
1197:
1193:
1189:
1185:
1180:
1176:
1172:
1168:
1161:
1156:
1152:
1138:
1118:
1110:
1094:
1074:
1066:
1062:
1058:
1057:vector spaces
1054:
1050:
1049:
1044:
1040:
1032:
1030:
1028:
1024:
1020:
1016:
1012:
1007:
1005:
1000:
996:
992:
991:string theory
985:
980:
975:
967:
965:
963:
959:
955:
951:
947:
942:
940:
937:
933:
929:
925:
921:
917:
909:
906:
904:
902:
897:
895:
891:
887:
883:
878:
876:
872:
868:
864:
860:
856:
852:
849:
845:
841:
837:
836:string theory
825:
820:
818:
813:
811:
806:
805:
803:
802:
797:
794:
792:
789:
788:
787:
786:
779:
776:
774:
771:
769:
766:
764:
763:Zamolodchikov
761:
759:
758:Zamolodchikov
756:
754:
751:
749:
746:
744:
741:
739:
736:
734:
731:
729:
726:
724:
721:
719:
716:
714:
711:
709:
706:
704:
701:
699:
696:
694:
691:
689:
686:
684:
681:
679:
676:
674:
671:
669:
666:
664:
661:
659:
656:
654:
651:
649:
646:
644:
641:
639:
636:
634:
631:
629:
626:
624:
621:
619:
616:
614:
611:
609:
606:
604:
601:
599:
596:
594:
591:
589:
586:
584:
581:
579:
576:
574:
571:
569:
566:
564:
561:
559:
556:
554:
551:
549:
546:
544:
541:
539:
536:
534:
531:
529:
526:
524:
521:
519:
516:
514:
511:
509:
506:
504:
501:
499:
496:
494:
491:
489:
486:
484:
481:
479:
476:
474:
471:
469:
466:
464:
461:
459:
456:
454:
451:
449:
446:
444:
441:
439:
436:
434:
431:
429:
426:
424:
421:
419:
416:
414:
411:
409:
406:
404:
401:
399:
396:
394:
391:
389:
386:
384:
381:
379:
376:
374:
371:
369:
366:
364:
361:
359:
356:
354:
351:
349:
346:
344:
341:
339:
336:
334:
331:
329:
326:
324:
321:
319:
316:
314:
311:
309:
306:
304:
301:
299:
296:
295:
289:
288:
281:
278:
276:
273:
271:
268:
266:
264:
260:
258:
255:
253:
250:
248:
247:Supersymmetry
245:
243:
240:
238:
235:
233:
230:
229:
223:
222:
217:
214:
212:
209:
207:
204:
202:
199:
197:
194:
193:
192:
191:
186:
181:
178:
176:
173:
171:
170:Phenomenology
168:
167:
166:
165:
162:Phenomenology
160:
155:
152:
150:
147:
145:
142:
140:
137:
135:
132:
130:
127:
126:
125:
124:
119:
113:
109:
105:
101:
98:
96:
93:
92:
91:
90:
85:
80:
77:
75:
72:
70:
69:Cosmic string
67:
65:
62:
61:
60:
59:
54:
50:
46:
45:
42:
41:String theory
38:
33:
19:
2988:Arkani-Hamed
2886:Supergravity
2853:Moduli space
2750:
2745:Dirac string
2671:Gauge theory
2651:Loop algebra
2588:Black string
2544:
2451:GS formalism
2254:
2231:
2219:. Retrieved
2214:
2210:
2181:
2154:
2136:
2127:
2118:
2109:
2100:
2091:
2082:
2073:
2064:
2055:
2046:
2037:
2028:
2019:
2010:
2001:
1996:(1988), 515.
1993:
1990:
1987:K. S. Stelle
1959:
1950:
1927:
1916:
1821:Econophysics
1769:Solar System
1654:Astrophysics
1434:
1366:Gauge theory
1235:
1204:
1164:
1046:
1042:
1036:
1019:gauge theory
1011:gauge theory
1008:
988:
953:
949:
945:
943:
938:
931:
930:is called a
927:
913:
907:
898:
879:
869:. They have
843:
833:
303:Arkani-Hamed
262:
252:Supergravity
73:
3348:Silverstein
2848:Orientifold
2583:Black holes
2578:Black brane
2535:Dual photon
2236:Basic Books
1991:Nucl. Phys.
1979: [
1801:Agrophysics
1745:Dark matter
1741:Dark energy
1513:Diffraction
1255:Black brane
954:worldvolume
848:dimensional
663:Silverstein
188:Mathematics
100:Superstring
3368:Strominger
3363:Steinhardt
3358:Staudacher
3273:Polchinski
3223:Nanopoulos
3183:Mandelstam
3163:Kontsevich
3003:Berenstein
2931:Holography
2911:Superspace
2810:K3 surface
2769:Worldsheet
2684:Instantons
2312:Background
1972:C. N. Pope
1964:M. J. Duff
1944:required.)
1833:Geophysics
1809:Biophysics
1725:Black hole
1663:Astrometry
1570:BCS theory
1419:Antimatter
1245:geometry.
936:M. J. Duff
882:categories
683:Strominger
678:Steinhardt
673:Staudacher
588:Polchinski
538:Nanopoulos
498:Mandelstam
478:Kontsevich
318:Berenstein
275:Multiverse
3403:Veneziano
3283:Rajaraman
3178:Maldacena
3068:Gopakumar
3018:Dijkgraaf
3013:Curtright
2679:Anomalies
2558:NS5-brane
2479:U-duality
2474:S-duality
2469:T-duality
1976:E. Sezgin
1909:Citations
1861:Photonics
1797:Acoustics
1777:Supernova
1667:Cosmology
1659:Astronomy
1627:Magnetism
1582:Fermi gas
1483:Photonics
1302:Concepts
1296:Subfields
1285:NS5-brane
1139:β
1119:α
1095:β
1075:α
1065:functions
1048:morphisms
941:in 1988.
924:drumheads
863:spacetime
859:dynamical
723:Veneziano
598:Rajaraman
493:Maldacena
383:Gopakumar
333:Dijkgraaf
328:Curtright
292:Theorists
180:Landscape
175:Cosmology
139:U-duality
134:T-duality
129:S-duality
112:Heterotic
3473:Category
3458:Zwiebach
3413:Verlinde
3408:Verlinde
3383:Townsend
3378:Susskind
3313:Sagnotti
3278:Polyakov
3233:Nekrasov
3198:Minwalla
3193:Martinec
3158:Knizhnik
3153:Klebanov
3148:Kapustin
3113:'t Hooft
3048:Fischler
2983:AganagiÄ
2954:M-theory
2843:Conifold
2838:Orbifold
2821:manifold
2762:Geometry
2568:M5-brane
2563:M2-brane
2500:Graviton
2416:F-theory
2202:(2005).
1968:T. Inami
1781:Universe
1700:Big Bang
1509:Molecule
1382:M-theory
1280:M5-brane
1275:M2-brane
1249:See also
1039:category
999:D-branes
984:D-branes
968:D-branes
922:such as
901:membrane
796:Glossary
778:Zwiebach
733:Verlinde
728:Verlinde
703:Townsend
698:'t Hooft
693:Susskind
628:Sagnotti
593:Polyakov
548:Nekrasov
513:Minwalla
508:Martinec
473:Knizhnik
468:Klebanov
463:Kapustin
433:Horowitz
363:Fischler
298:AganagiÄ
216:K-theory
149:F-theory
144:M-theory
18:P-branes
3388:Trivedi
3373:Sundrum
3338:Shenker
3328:Seiberg
3323:Schwarz
3293:Randall
3253:Novikov
3243:Nielsen
3228:NÄstase
3138:Kallosh
3123:Gibbons
3063:Gliozzi
3053:Friedan
3043:Ferrara
3028:Douglas
3023:Distler
2573:S-brane
2553:D-brane
2510:Tachyon
2505:Dilaton
2319:Strings
2221:June 7,
1923:"brane"
1753:Gravity
1308:Nuclear
1179:charges
1043:objects
974:D-brane
910:-branes
791:History
708:Trivedi
688:Sundrum
653:Shenker
643:Seiberg
638:Schwarz
608:Randall
568:Novikov
558:Nielsen
543:NÄstase
453:Kallosh
438:Gibbons
378:Gliozzi
368:Friedan
358:Ferrara
343:Douglas
338:Distler
108:Type II
95:Bosonic
79:D-brane
3453:Zumino
3448:Zaslow
3433:Yoneya
3423:Witten
3343:Siegel
3318:Scherk
3288:Ramond
3263:Ooguri
3188:Marolf
3143:Kaluza
3128:Kachru
3118:HoĆava
3108:Harvey
3103:Hanson
3088:Gubser
3078:Greene
3008:Bousso
2993:Atiyah
2545:Branes
2355:Theory
2263:
2242:
2188:
2169:
1985:, and
1853:Optics
1765:Planet
1749:Galaxy
1737:Cosmos
1623:Phonon
1607:liquid
1599:Phases
1501:Photon
1479:Optics
1439:String
1407:strong
1109:states
995:string
958:fields
939:et al.
875:charge
855:string
773:Zumino
768:Zaslow
753:Yoneya
743:Witten
658:Siegel
633:Scherk
603:Ramond
578:Ooguri
503:Marolf
458:Kaluza
443:Kachru
428:HoĆava
423:Harvey
418:Hanson
403:Gubser
393:Greene
323:Bousso
308:Atiyah
104:Type I
64:String
3393:Turok
3303:RoÄek
3268:Ovrut
3258:Olive
3238:Neveu
3218:Myers
3213:Mukhi
3203:Moore
3173:Linde
3168:Klein
3093:Gukov
3083:Gross
3073:Green
3058:Gates
3038:Dvali
2998:Banks
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2207:(PDF)
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1611:solid
1521:Laser
1435:Brane
1293:Field
1059:, or
1021:and
844:brane
842:), a
713:Turok
618:RoÄek
583:Ovrut
573:Olive
553:Neveu
533:Myers
528:Mukhi
518:Moore
488:Linde
483:Klein
408:Gukov
398:Gross
388:Green
373:Gates
353:Dvali
313:Banks
74:Brane
3418:Wess
3398:Vafa
3308:Rohm
3208:Motl
3133:Kaku
3098:Guth
3033:Duff
2261:ISBN
2240:ISBN
2223:2018
2186:ISBN
2167:ISBN
1994:B297
1773:Star
1647:Spin
1505:Atom
1415:Spin
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