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Vafa C., Zaslow E. — Mirror symmetry
Vafa C., Zaslow E. — Mirror symmetry

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Название: Mirror symmetry

Авторы: Vafa C., Zaslow E.

Аннотация:

This thorough and detailed exposition is the result of an intensive month-long course sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives. The material will be particularly useful for those wishing to advance their understanding by exploring mirror symmetry at the interface of mathematics and physics.
This one-of-a-kind volume offers the first comprehensive exposition on this increasingly active area of study. It is carefully written by leading experts who explain the main concepts without assuming too much prerequisite knowledge. The book is an excellent resource for graduate students and research mathematicians interested in mathematical and theoretical physics.


Язык: en

Рубрика: Математика/Математическая Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 457

Добавлена в каталог: 26.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\overline{\partial}$-operator      71 731 735
A-brane      800 813 847 856 861
A-cycle      707
A-model      87 647 658 661 671 688 730
A-twist      401 408 586 850 855 856
action      146
ADE singularity      99 337 677
Adjunction formula      53 521 667
Affine structure      703
ALE space      372
Almost complex structure      68 487 488 627
Almost complex structure, integrable      488
angular momentum      282
Annulus amplitude      657 661
Anomaly      295 833
Anomaly, axial      353 589 813
Anomaly, factorization      660
Anomaly, holomorphic      593 597 654 657 662 668 672
Anomaly, Quillen      597 646 656
Anomaly, R-anomaly      809
Anomaly-free      809
Anti-brane      708 739
Anti-chiral superfield      273
Anti-chiral superfield, twisted      274
Anti-topological theory      427
Arithmetic genus      490
Aspinwall — Morrison formula      537 546 635
asymptotic freedom      366
Atiyah — Bott fixed-point theorem      58
Autoequivalence      760
Auxiliary field      277
B-brane      800 805 838 847 855 856 872
B-cycle      707
B-field      254 294 687 798 803 806 867
B-model      87 654 655 657 658 685 686 730
B-twist      401 416 420 592 850 856
Bare coupling      325
Bare field      325
Batyrev's construction      665
Bekenstein — Hawking entropy      612
Beltrami differential      422 590 596
Bernoulli number      552 610 638
beta function      326 327 329
Bianchi identity      50 75 247 252
Black hole      612
Black hole, entropy      695
Blow-down      126
Blow-up      97 123—125 369
Boson-fermion equivalence      266
Bosonic      155
Bott residue formula      537
Bott — Morse function      233 303
Bound state      704
Boundary condition      450 766ff
Boundary condition, Dirichlet      450 659 767ff
Boundary condition, Neumann      450 659 767ff
Boundary condition, twisted      259
Boundary divisor      500 510
Boundary field theory      697
Boundary lemma      513
Boundary state      454 779 847ff
Boundary stratum      499
BPS, configuration      447 469
BPS, soliton      435ff 436 447 470
BPS, state      606 607 615 616 619 636 671 694
Bubbling      499 513
Bundle, polystable      736 737 743 744 755
Bundle, semistable      736 744
c-theorem      790
Calabi — Yau      see "Calabi — Yau manifold"
Calabi — Yau condition      74
Calabi — Yau correspondence      393
Calabi — Yau form      91
Calabi — Yau hypersurface      130
Calabi — Yau manifold      55 64 72 77 299 329 337 416 434 464 523 571ff 587 720 761 851 857
Calabi — Yau manifold, mirror      603
Calabi — Yau manifold, non-compact      474 842
Calabi — Yau moduli space      78 82
Calabi — Yau n-fold      455 654 816 867
Calabi — Yau threefold      130 548 562 587 589 600 617 625 630 662 679 853
Cardy's construction      871
Cech cohomology      34
Cech — de Rham cohomology      36
Cech — Dolbeault isomorphism      37 81
Characteristic class      45
Charge      114 115
Charge fractionalization      390
Charge lattice      859
Charge, central      283 693 790 870
Charge, conserved      208 214 279 776
Charge, R-charge      826 830 836 863
Chern character      51 704 740
Chern class      45ff 297 317 810
Chern — Simons theory      680 684—687 690
Chern — Simons theory, holomorphic      705
Chiral field      164
Chiral field, twisted      466
Chiral multiplet      284 351 472
Chiral multiplet, twisted      284
Chiral operator      398
Chiral operator, twisted      398
Chiral ring      164 165 337 397ff 404ff
Chiral ring, twisted      398
Chiral superfield      273 335 435
Chiral superfield, twisted      281 382
Chow group      116
Chow ring      485
Classifying space      58
Clemens conjecture      561
Clifford algebra      254
Coherent sheaf      707 708 736 739
Comparison lemma      513 528
Complete conic      502
Complete intersection      374 377
Complex manifold      78
Complex of sheaves      740
Complex structure      67 70
Complex submanifold      806
Compton wavelength      327
Cone      102 105 108 122
Cone, polyhedral      102
confinement      381
Conformal field theory      335
Conformal structure      487
Conifold      95 684
Conifold, transition      98
Conjugate momentum      174 769
Connect sum      758 759 763
Connection      13
Connection, HYM      731 735 743 762
Connection, Levi — Civita      15
Conservation equation      238
Conserved current      239 279 293
coordinates      4 25
Coordinates, flat      457 588
Coordinates, homogeneous      25 105 123 133
Correlation function      163 410 418 421
Correlation function, topological      404 418
Correlator      553 560 562 564 571 577
Correspondence principle      724
Cotangent bundle      9
Cotangent bundle, holomorphic      69
Crepant resolution      95
Critical point      197 202 205 836 847
Curvature      16
D-brane      449ff 606 684 692ff 709 729ff 742 767
D-brane, worldvolume      696
D-term      274 331 438 463
D2-brane      609 615 618
de Rham, cohomology      20 71 210 410
de Rham, cohomology complex      19
Decoupling      331
Dedekind eta function      246 650 771
Deformation      161
Deformation of complex structures      79
Deformation theory      504
Deformation, conifold      96
Deformation, Hamiltonian      751 752 755 760
Deformation, invariance      160
Deformation, long exact sequence      506
Deformation, obstructions to      505 748
Deformation, unobstructed      748
Degeneration      495
Dehn twist      757 760
Del Pezzo surface      369
Deligne — Mumford stack      484 541 542 572
Derived category      708 719 730 738ff
Derived category, autoequivalence      739
Derived category, inverting arrows in      741
Descendant invariant      526ff 557
Determinant      660
Differential form      10 18
Dilaton equation      514 527
Dimensional transmutation      331 354
Dirac fermion      254 260 278 768 775 782 787
Dirac operator      411 660 827
Dirac — Born — Infeld action      700
Dirac's sea      259
Divisor      39
Divisor equation      527
Divisor, T-invariant      107 108 129 136
Dolbeault cohomology      41 58 839
Dolbeault operator      215 410 812
Donaldson — Uhlenbeck — Yau theorem      736
Dual graph      489
Dualizing sheaf      492
Dynkin diagram      99 677
EDGE      103 105 106
Effective action      325 382
Elliptic curve      78 495 591 641 714 762
Elliptic fibration      130 667
Elliptic rational surface      643
Entropy, boundary      791 793
Entropy, bounded      789
Enumerative prediction      672 673
Equation of motion      170 252 326 449
Equivariant cohomology      58ff 62 535ff 566
Euler characteristic      18 45 58 191 589 610 625 626
Euler class      45 63 523 550 617
Euler — Lagrange equation      170
Evaluation map      503
Exceptional collection      869
Exceptional divisor      97 370
Exceptional pair      868
Exceptional sheaf      868
Excess intersection      47 65
Excess intersection, formula      525
Extension class of sheaves      743
Extensions of holomorphic bundles      737
F-term      275 331 387 463 602 604 608
F-term, twisted      275 331 405
F-theory      130
Fan      101ff 115 128 131
Fan, morphism of      127
Fan, normal      133
Fan, simplicial      124
Fano manifold      365 559 568 640 868
Fayet — Iliopoulos (FI) parameter      112 118 351 353 465
Fermat quintic      478
Fermion number operator      185
Fermionic      155
Feynman diagram      152 154 172 320 585 599 681 683
Feynman graph      681 692
Fixed point      57
Flag      542 543
Flat U(1) connection      747
Floer cohomology      749 832 838
Floer homology      831
FLOP      125
Forgetful map      528
Forgetful morphism      498 503
Fourier — Mukai transform      708 723 739
Free energy      154
Free energy of a point      515
frequency      314
Frobenius manifold      87
Fubini — Study metric      359 360
Fukaya composition      719
Fukaya's $A^{\infty}$ category      710 730 745
Fulton — MacPherson configuration space      502
Fundamental solution      555
g-theorem      791
Gauge field      146 296 342 800
Gauge symmetry      341
Gauss — Manin connection      84 430
Gaussian measure      153
Generating function      647
Geometric engineering      108 130 677
Gerbe      707
Givental's polynomiality condition      577
GKO construction      870
GKZ decomposition      113 118
Goldstone boson      344
Goldstone mode      344
Goldstone's theorem      344
Gopakumar — Vafa invariant      611 615ff 635ff 670
Graded Lagrangian      715
Gradient flow      44 737 836
Grading      745 754 759
Grassmann variables      155
Grassmannian      329 502
Grassmannian, Lagrangian      815 818
Gravitational descendant      725
Gravitational invariant      526
Gromov — Witten invariant      64 94 526ff 546 550 564 611 617 619 627 633 635 640 647 671
Gromov — Witten invariant, open string      706
Gromov — Witten potential      635 637
Gromov — Witten theory      615 627
Grothendieck — Riemann — Roch formula      52 56 488 717
Ground state      306 307
Ground state, Ramond — Ramond (RR)      645
Ground state, RR, overlap with      849 878
Group cohomology      58
GSO projection      266 872
Hamiltonian      147 171 173 174 282
Hamiltonian deformation      745 746
harmonic oscillator      239
Harmonic oscillator, simple      174
Harmonic oscillator, supersymmetric      194
Helix      869
Hermitian metric      70
Hermitian symmetric space      329
Hermitian — Yang — Mills connection      697 730 731 733 see "HYM
hessian      201 303 664 859
Higgs mechanism      346 704
Hilbert scheme      623 625 630
Hirzebruch surface      29 106 371
Hirzebruch — Riemann — Roch theorem      586
Hitchin — Kobayashi correspondence      761
Hochschild cohomology      725
Hodge bundle      83 84 86 516 550
Hodge decomposition      22
Hodge numbers      71
Hodge star      21
Hodge theory      22
Holomorphic bundle      730 739 855 867 884
Holomorphic Casson invariant      747
Holomorphic Chern — Simons functional      749 750
Holomorphic vector field      57 217
Holomorphic vector field, zeroes      57
1 2 3
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