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Witten index

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401: 458: 296: 313:. A more refined invariant in 2-dimensional theories, constructed using only the right-moving part of the fermion number operator together with a 2-parameter family of variations, is the 105: 140:
contains an equal number of bosonic and fermionic states. Because of this, the Witten index is independent of the temperature and gives the number of zero energy bosonic
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It is an example of a quasi-topological quantity, which is a quantity that depends only on
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then there are no zero energy ground states and so the Witten index is equal to zero.
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minus the number of zero energy fermionic vacuum states. In particular, if
141: 152: 137: 115: 111: 306: 302: 457: 168: 48: 121:. This is what makes it different from the ordinary 290: 99: 510: 35:β is defined as a modification of the standard 493: 436: 327:Supersymmetric theory of stochastic dynamics 500: 486: 443: 429: 232: 155:on a manifold is given by the manifold's 151:The Witten index of the supersymmetric 511: 382:Constraints on Supersymmetry Breaking 146:supersymmetry is spontaneously broken 125:. It is sometimes referred to as the 452: 395: 519:Supersymmetric quantum field theory 13: 14: 550: 456: 399: 339: 279: 273: 248: 238: 214: 189: 179: 176: 100:{\displaystyle {\textrm {Tr}}} 94: 69: 59: 56: 1: 332: 472:. You can help Knowledge by 415:. You can help Knowledge by 136:theory, each nonzero energy 7: 534:Statistical mechanics stubs 320: 16:Modified partition function 10: 555: 451: 394: 114:operator, where F is the 468:-related article is a 292: 101: 539:Quantum physics stubs 529:Statistical mechanics 409:statistical mechanics 293: 102: 25:statistical mechanics 524:Quantum field theory 166: 157:Euler characteristic 46: 21:quantum field theory 407:This article about 33:inverse temperature 288: 237: 127:spectral asymmetry 123:partition function 97: 37:partition function 481: 480: 466:quantum mechanics 424: 423: 367:978-0-8218-2955-4 284: 220: 173: 53: 546: 502: 495: 488: 460: 453: 445: 438: 431: 403: 396: 373: 371: 343: 297: 295: 294: 289: 282: 266: 265: 256: 255: 236: 235: 213: 212: 197: 196: 175: 174: 171: 106: 104: 103: 98: 93: 92: 77: 76: 55: 54: 51: 554: 553: 549: 548: 547: 545: 544: 543: 509: 508: 507: 506: 450: 449: 392: 384:, Nucl. Phys. 377: 376: 368: 353:Mirror Symmetry 344: 340: 335: 323: 261: 257: 251: 247: 231: 224: 202: 198: 192: 188: 170: 169: 167: 164: 163: 119:number operator 82: 78: 72: 68: 50: 49: 47: 44: 43: 17: 12: 11: 5: 552: 542: 541: 536: 531: 526: 521: 505: 504: 497: 490: 482: 479: 478: 461: 448: 447: 440: 433: 425: 422: 421: 404: 390: 389: 388:(1982) 253-316 380:Edward Witten 375: 374: 366: 337: 336: 334: 331: 330: 329: 322: 319: 315:elliptic genus 299: 298: 287: 281: 278: 275: 272: 269: 264: 260: 254: 250: 246: 243: 240: 234: 230: 227: 223: 219: 216: 211: 208: 205: 201: 195: 191: 187: 184: 181: 178: 134:supersymmetric 108: 107: 96: 91: 88: 85: 81: 75: 71: 67: 64: 61: 58: 15: 9: 6: 4: 3: 2: 551: 540: 537: 535: 532: 530: 527: 525: 522: 520: 517: 516: 514: 503: 498: 496: 491: 489: 484: 483: 477: 475: 471: 467: 462: 459: 455: 454: 446: 441: 439: 434: 432: 427: 426: 420: 418: 414: 410: 405: 402: 398: 397: 393: 387: 383: 379: 378: 372:p191 (10.124) 369: 363: 359: 355: 354: 349: 348:Hori, Kentaro 342: 338: 328: 325: 324: 318: 316: 312: 308: 304: 285: 276: 270: 267: 262: 258: 252: 244: 241: 228: 225: 221: 217: 209: 206: 203: 199: 193: 185: 182: 162: 161: 160: 158: 154: 149: 147: 143: 142:vacuum states 139: 135: 130: 128: 124: 120: 117: 113: 89: 86: 83: 79: 73: 65: 62: 42: 41: 40: 38: 34: 30: 26: 22: 474:expanding it 463: 417:expanding it 406: 391: 385: 381: 351: 341: 300: 150: 131: 109: 29:Witten index 28: 18: 305:and not on 153:sigma model 513:Categories 333:References 311:Lagrangian 138:eigenvalue 271:χ 242:− 229:∈ 222:∑ 207:β 204:− 183:− 110:Note the 87:β 84:− 63:− 321:See also 309:in the 307:D-terms 303:F-terms 116:fermion 31:at the 364:  283:  27:, the 464:This 411:is a 132:In a 470:stub 413:stub 386:B202 362:ISBN 358:CIMM 112:(-1) 23:and 360:1. 19:In 515:: 356:. 345:* 317:. 172:Tr 159:. 129:. 52:Tr 39:: 501:e 494:t 487:v 476:. 444:e 437:t 430:v 419:. 370:. 286:. 280:) 277:M 274:( 268:= 263:p 259:b 253:p 249:) 245:1 239:( 233:Z 226:p 218:= 215:] 210:H 200:e 194:F 190:) 186:1 180:( 177:[ 95:] 90:H 80:e 74:F 70:) 66:1 60:( 57:[

Index

quantum field theory
statistical mechanics
inverse temperature
partition function
(-1)
fermion
number operator
partition function
spectral asymmetry
supersymmetric
eigenvalue
vacuum states
supersymmetry is spontaneously broken
sigma model
Euler characteristic
F-terms
D-terms
Lagrangian
elliptic genus
Supersymmetric theory of stochastic dynamics
Hori, Kentaro
Mirror Symmetry
CIMM
ISBN
978-0-8218-2955-4
Stub icon
statistical mechanics
stub
expanding it
v

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