Knowledge (XXG)

Supergeometry

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129: 92: 255: 225: 198: 636: 732: 484: 783: 295: 275: 768: 758: 737: 778: 277:-supermanifolds, and DeWitt supermanifolds. In particular, supervector bundles and principal superbundles are considered in the category of 788: 477: 432: 409: 387: 904: 793: 517: 360: 831: 826: 297:-supermanifolds. Definitions of principal superbundles and principal superconnections straightforwardly follow that of smooth 1066: 763: 470: 302: 144: 727: 651: 811: 696: 512: 711: 681: 565: 706: 132: 31: 329: 140: 1061: 816: 666: 570: 43: 753: 691: 846: 841: 595: 575: 448: 420: 23: 105: 68: 631: 580: 95: 27: 851: 836: 821: 590: 99: 230: 960: 532: 527: 452: 203: 176: 428: 405: 383: 170: 136: 320:
superbundles and superconnections. These superconnections have been applied to computing the
661: 560: 547: 317: 298: 990: 955: 676: 671: 350: 306: 158: 150: 47: 39: 1020: 1010: 995: 641: 626: 333: 313: 280: 260: 55: 1055: 1035: 1015: 965: 600: 507: 493: 355: 345: 166: 154: 51: 35: 1040: 1025: 985: 975: 970: 861: 803: 686: 555: 522: 397: 59: 1030: 1005: 1000: 950: 929: 894: 889: 616: 365: 321: 173:. There are different types of supermanifolds. These are smooth supermanifolds ( 934: 924: 909: 701: 621: 585: 980: 884: 773: 919: 914: 899: 874: 325: 162: 879: 139:
on these modules and sheaves. However, supergeometry is not particular
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also are phrased in terms of sheaves of graded commutative algebras.
869: 456: 305:. Principal graded bundles also are considered in the category of 42:. Supergeometry is part and parcel of many classical and quantum 462: 466: 378:
Bartocci, C.; Bruzzo, U.; Hernandez Ruiperez, D. (1991),
283: 263: 233: 206: 179: 108: 71: 943: 860: 802: 746: 720: 609: 546: 500: 289: 269: 249: 219: 192: 135:). In particular, superconnections are defined as 123: 86: 425:Connections in Classical and Quantum Field Theory 143:because of a different definition of a graded 478: 8: 485: 471: 463: 282: 262: 241: 232: 211: 205: 184: 178: 115: 111: 110: 107: 78: 74: 73: 70: 169:are constructed by gluing of sheaves of 65:Supergeometry is formulated in terms of 402:Supermanifolds: Theory and Applications 16:Differential geometry of supermanifolds 7: 242: 212: 185: 14: 518:Supersymmetric quantum mechanics 361:Connection (algebraic framework) 161:are characterized by sheaves on 124:{\displaystyle \mathbb {Z} _{2}} 87:{\displaystyle \mathbb {Z} _{2}} 380:The Geometry of Supermanifolds 312:There is a different class of 131:-graded commutative algebras ( 1: 451:, Lectures on supergeometry, 250:{\displaystyle GH^{\infty }} 513:Supersymmetric gauge theory 220:{\displaystyle G^{\infty }} 193:{\displaystyle H^{\infty }} 32:graded commutative algebras 1083: 812:Pure 4D N = 1 supergravity 712:Electric–magnetic duality 133:supercommutative algebras 733:Haag–ƁopuszaƄski–Sohnius 707:Little hierarchy problem 789:6D (2,0) superconformal 330:noncommutative geometry 141:noncommutative geometry 769:N = 4 super Yang–Mills 759:N = 1 super Yang–Mills 667:Supersymmetry breaking 571:Superconformal algebra 566:Super-PoincarĂ© algebra 291: 271: 251: 221: 194: 125: 88: 1067:Differential geometry 847:Type IIB supergravity 842:Type IIA supergravity 817:4D N = 1 supergravity 682:Seiberg–Witten theory 596:Super Minkowski space 576:Supersymmetry algebra 303:principal connections 292: 272: 252: 222: 195: 126: 89: 24:differential geometry 632:Short supermultiplet 427:, World Scientific, 404:, World Scientific, 281: 261: 231: 204: 177: 106: 69: 852:Gauged supergravity 837:Type I supergravity 794:ABJM superconformal 591:Harmonic superspace 827:Higher dimensional 822:N = 8 supergravity 738:Nonrenormalization 533:Super vector space 528:Superstring theory 287: 267: 257:-supermanifolds), 247: 217: 190: 171:supervector spaces 137:Koszul connections 121: 84: 1049: 1048: 692:Wess–Zumino gauge 419:Mangiarotti, L.; 299:principal bundles 290:{\displaystyle G} 270:{\displaystyle G} 1074: 832:11D supergravity 561:Lie superalgebra 548:Supermathematics 487: 480: 473: 464: 449:G. Sardanashvily 437: 414: 392: 307:graded manifolds 296: 294: 293: 288: 276: 274: 273: 268: 256: 254: 253: 248: 246: 245: 226: 224: 223: 218: 216: 215: 199: 197: 196: 191: 189: 188: 163:smooth manifolds 159:Graded manifolds 151:Graded manifolds 130: 128: 127: 122: 120: 119: 114: 93: 91: 90: 85: 83: 82: 77: 40:graded manifolds 1082: 1081: 1077: 1076: 1075: 1073: 1072: 1071: 1052: 1051: 1050: 1045: 939: 856: 798: 742: 728:Coleman–Mandula 716: 677:Seiberg duality 672:Konishi anomaly 605: 542: 496: 491: 445: 435: 418: 412: 396: 390: 377: 374: 351:Graded manifold 342: 322:Chern character 279: 278: 259: 258: 237: 229: 228: 207: 202: 201: 180: 175: 174: 109: 104: 103: 72: 67: 66: 17: 12: 11: 5: 1080: 1078: 1070: 1069: 1064: 1054: 1053: 1047: 1046: 1044: 1043: 1038: 1033: 1028: 1023: 1018: 1013: 1008: 1003: 998: 993: 988: 983: 978: 973: 968: 963: 958: 953: 947: 945: 941: 940: 938: 937: 932: 927: 922: 917: 912: 907: 902: 897: 892: 887: 882: 877: 872: 866: 864: 858: 857: 855: 854: 849: 844: 839: 834: 829: 824: 819: 814: 808: 806: 800: 799: 797: 796: 791: 786: 781: 776: 771: 766: 761: 756: 750: 748: 747:Field theories 744: 743: 741: 740: 735: 730: 724: 722: 718: 717: 715: 714: 709: 704: 699: 694: 689: 684: 679: 674: 669: 664: 659: 654: 649: 644: 642:Superpotential 639: 634: 629: 627:Supermultiplet 624: 619: 613: 611: 607: 606: 604: 603: 598: 593: 588: 583: 578: 573: 568: 563: 558: 552: 550: 544: 543: 541: 540: 535: 530: 525: 520: 515: 510: 504: 502: 501:General topics 498: 497: 492: 490: 489: 482: 475: 467: 461: 460: 444: 443:External links 441: 440: 439: 433: 416: 410: 394: 388: 373: 370: 369: 368: 363: 358: 353: 348: 341: 338: 334:BRST formalism 286: 266: 244: 240: 236: 214: 210: 187: 183: 167:supermanifolds 155:supermanifolds 118: 113: 81: 76: 54:field theory, 46:involving odd 44:field theories 36:supermanifolds 15: 13: 10: 9: 6: 4: 3: 2: 1079: 1068: 1065: 1063: 1062:Supersymmetry 1060: 1059: 1057: 1042: 1039: 1037: 1034: 1032: 1029: 1027: 1024: 1022: 1019: 1017: 1014: 1012: 1009: 1007: 1004: 1002: 999: 997: 994: 992: 989: 987: 984: 982: 979: 977: 974: 972: 969: 967: 964: 962: 959: 957: 954: 952: 949: 948: 946: 942: 936: 933: 931: 928: 926: 923: 921: 918: 916: 913: 911: 908: 906: 903: 901: 898: 896: 893: 891: 888: 886: 883: 881: 878: 876: 873: 871: 868: 867: 865: 863: 862:Superpartners 859: 853: 850: 848: 845: 843: 840: 838: 835: 833: 830: 828: 825: 823: 820: 818: 815: 813: 810: 809: 807: 805: 801: 795: 792: 790: 787: 785: 782: 780: 777: 775: 772: 770: 767: 765: 762: 760: 757: 755: 752: 751: 749: 745: 739: 736: 734: 731: 729: 726: 725: 723: 719: 713: 710: 708: 705: 703: 700: 698: 695: 693: 690: 688: 685: 683: 680: 678: 675: 673: 670: 668: 665: 663: 660: 658: 655: 653: 650: 648: 645: 643: 640: 638: 635: 633: 630: 628: 625: 623: 620: 618: 615: 614: 612: 608: 602: 601:Supermanifold 599: 597: 594: 592: 589: 587: 584: 582: 579: 577: 574: 572: 569: 567: 564: 562: 559: 557: 554: 553: 551: 549: 545: 539: 538:Supergeometry 536: 534: 531: 529: 526: 524: 521: 519: 516: 514: 511: 509: 508:Supersymmetry 506: 505: 503: 499: 495: 494:Supersymmetry 488: 483: 481: 476: 474: 469: 468: 465: 458: 454: 450: 447: 446: 442: 436: 434:981-02-2013-8 430: 426: 423:, G. (2000), 422: 421:Sardanashvily 417: 413: 411:981-02-1228-3 407: 403: 399: 395: 391: 389:0-7923-1440-9 385: 381: 376: 375: 371: 367: 364: 362: 359: 357: 356:Supersymmetry 354: 352: 349: 347: 346:Supermanifold 344: 343: 339: 337: 335: 331: 327: 323: 319: 315: 310: 308: 304: 300: 284: 264: 238: 234: 208: 181: 172: 168: 164: 160: 156: 152: 148: 146: 142: 138: 134: 116: 101: 97: 79: 63: 61: 57: 53: 49: 45: 41: 37: 33: 29: 25: 21: 20:Supergeometry 804:Supergravity 697:Localization 687:Witten index 662:Moduli space 556:Superalgebra 537: 523:Supergravity 424: 401: 379: 311: 149: 64: 60:supergravity 19: 18: 944:Researchers 930:Stop squark 895:Graviscalar 890:Graviphoton 754:Wess–Zumino 617:Supercharge 366:Supermetric 56:BRST theory 1056:Categories 991:Iliopoulos 935:Superghost 925:Sgoldstino 910:Neutralino 702:Mu problem 622:R-symmetry 586:Superspace 581:Supergroup 398:Rogers, A. 382:, Kluwer, 372:References 145:derivation 961:Batchelor 885:Goldstino 774:Super QCD 652:FI D-term 637:BPS state 457:0910.0092 243:∞ 213:∞ 186:∞ 996:Montonen 920:Sfermion 915:R-hadron 900:Higgsino 875:Chargino 764:4D N = 1 721:Theorems 610:Concepts 400:(2007), 340:See also 326:K-theory 165:, while 94:-graded 50:, e.g., 1011:Seiberg 986:Golfand 966:Berezin 951:Affleck 880:Gaugino 318:Ne'eman 314:Quillen 100:sheaves 96:modules 28:modules 1041:Zumino 1036:Witten 1026:Rogers 1016:Siegel 956:Bagger 657:F-term 647:D-term 431:  408:  386:  332:, and 48:fields 1021:Roček 1006:Salam 1001:Olive 981:Gates 976:Fayet 870:Axino 784:NMSSM 453:arXiv 102:over 58:, or 30:over 1031:Wess 971:Dine 779:MSSM 429:ISBN 406:ISBN 384:ISBN 301:and 153:and 98:and 52:SUSY 38:and 905:LSP 324:in 227:-, 200:-, 26:of 22:is 1058:: 336:. 328:, 309:. 147:. 62:. 34:, 486:e 479:t 472:v 459:. 455:: 438:. 415:. 393:. 316:– 285:G 265:G 239:H 235:G 209:G 182:H 117:2 112:Z 80:2 75:Z

Index

differential geometry
modules
graded commutative algebras
supermanifolds
graded manifolds
field theories
fields
SUSY
BRST theory
supergravity
modules
sheaves
supercommutative algebras
Koszul connections
noncommutative geometry
derivation
Graded manifolds
supermanifolds
Graded manifolds
smooth manifolds
supermanifolds
supervector spaces
principal bundles
principal connections
graded manifolds
Quillen
Ne'eman
Chern character
K-theory
noncommutative geometry

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