Abstract
We give an overview of recent work on Dirichlet branes on CalabiYau threefolds which makes contact with Kontsevich’s homological mirror symmetry proposal, proposes a new definition of stability which is appropriate in string theory, and provides concrete quiver categories equivalent to certain categories of branes on CY.
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References
A. A. BeilinsonCoherent sheaves on P f and problems of linear algebra, Funct. Anal. Appl.12(1978) 214–216.
A. A. Beilinson, Bernstein and P. DeligneFaiseaux PerversAsterisque 100 (1982).
T. Bridgeland, A. King, and M. ReidMukai implies McKaymath.AG/9908027.
I. Brunner, M. R. Douglas, A. Lawrence, and C. RömelsbergerD-braves on the quinticto appear in J. High Energy Physics, hep-th/9906200.
P. Candelas, X. de la Ossa, A. Font, S. Katz, and D. R. MorrisonMirror symmetry for two parameter models - INucl. Phys. B416 (1994) 481, hep-th/9308083.
P. Candelas, X. C. de la Ossa, P. S. Green, and L. ParkesA pair of Calabi-Yau manifolds as an exactly soluble superconformal theoryNucl. Phys. B359 (1991) 21.
D. A. Cox and S. KatzMirror Symmetry and Algebraic GeometryMathematical Surveys 68 1999, AMS.
J. Dai, R. G. Leigh andJ.PolchinskiNew Connections Between String TheoriesMod. Phys. Lett.A42073 (1989).
R. DijkgraafFields Strings and Dualityin Les Houches LXIV,Symetries Quantiqueseds. A. Connes, K. Gawedzki and J. Zinn-Justin, Elsevier (1998).
S. Donaldson and R. Thomas, Gauge Theory in Higher Dimensions, in The Geometric Universe; Science, Geometry, and the Work of Roger Penrose, Oxford University Press, 1998.
M. R. Douglas and G. MooreD-branes Quivers and ALE Instantons hepth/9603167.
M. R. Douglas, B. R. Greene, and D. R. MorrisonOrbifold resolution by D-branesNucl. Phys. B506 (1997) 84, hep-th/9704151.
M. R. Douglas and B. R. GreeneMetrics on D-brave orbifoldsAdv. Theor. Math. Phys. 1 184 (1998) hep-th/9707214.
M. R. DouglasTwo Lectures on D-Geometry and Noncommutative Geometryin Nonperturbative Aspects of Strings Branes and SupersymmetryWorld Scientific (1999), hep-th/9901146.
M. R. DouglasTopics in D-geometryClass. Quant. Gray. 17 (2000) 1057, hepth/9910170.
M. R. Douglas, B. Fiol, and C. RömelsbergerStability and BPS braneshepth/0002037.
M. R. Douglas, B. Fiol, and C. RömelsbergerThe spectrum of BPS branes on a noncompact Calabi-Yau hep-th/0003263.
M. R. Douglas and D.-E. DiaconescuD-branes on Stringy Calabi-Yau Manifolds hep-th/0006224.
M. R. DouglasD-branes Categories and N =1 Supersymmetry to appear.
] M. R. Douglas and D.-E. Diaconescu, to appear.
B. Fiol and M. MarinoBPS states and algebras from quiversJHEP 0007 (2000) 031, hep-th/0006189.
R. Gopakumar and C. VafaM-Theory and Topological Strings-Ihep-th/9809187.
S. Govindarajan, T. Jayaraman, and T. SarkarWorld sheet approaches to D-branes on supersymmetric cycles hep-th/9907131.
B. R. GreeneString theory on Calabi-Yau manifolds hep-th/9702155.
B. R. Greene and M. R. PlesserDuality in Calabi-Yau Moduli Space, Nucl. Phys.B338 (1990) 15.
M. T. Grisaru, A. E. van de Ven and D. ZanonTwo-Dimensional Supersymmetric Sigma Models On Ricci-Flat Kahler Manifolds Are Not Finite, Nucl. Phys.B277 (1986), 388.
M. GrossTopological Mirror Symmetrymath.AG/9909015.
F. Reese HarveySpinors and CalibrationsAcademic Press (1990).
J.A. Harvey and G. MooreOn the algebras of BPS statesComm. Math. Phys. 197 489 (1998), hep-th/9609017.
K. Hori, A. Iqbal, and C. VafaD-braves and mirror symmetryhep-th/0005247.
R. P. HorjaHypergeometric functions and mirror symmetry in toric varietiesmath.AG/9912109.
Y. Ito and H. NakajimaMcKay correspondence and Hilbert schemes in dimension threemath.AG/9803120.
I.Jack, D. R. Jones and J. Panvel, Six loop divergences in the supersymmetric Kahler sigma model, Int. J. Mod. Phys. A82591 (1993); hep-th/9311117.
D. JoyceOn counting special Lagrangian homology 3-sphereshep-th/9907013.
S. Kachru, S. Katz, A. Lawrence and J. McGreevyMirror Symmetry for Open Stringshep-th/0006047.
M. KontsevichHomological Algebra of Mirror SymmetryProceedings of the 1994 ICM, alg-geom/9411018.
P. B. KronheimerThe construction of ALE spaces as hyper-Kähler quotientsJ. Diff. Geom. 29 (1989) 665.
N. C. LeungEinstein Type Metrics and Stability on Vector BundlesJ. Diff. Geom.45 (1997) 514.
N. C. Leung, S.-T. Yau and E. ZaslowFrom Special Lagrangian to Hermitian-YangMills via Fourier-Mukai Transformmath.DG/0005118.
M. Marino, R. Minasian, G. Moore and A. StromingerNonlinear Instantons from Supersymmetric p-BranesJHEP 0001 (2000) 005, hep-th/9911206.
D. R. MorrisonGeometric Aspects of Mirror Symmetrymath.AG/0007090.
K.S. Narain, M.H. Sarmadi and C. Vafa(Harvard U.),Asymmetric orbifoldsNucl. Phys. B288 (1987), 551.
D. Nemeschansky and A. SenConformal Invariance Of Supersymmetric Sigma Models On Calabi-Yau Manifolds Phys. Lett. B178 (1986), 365.
H. Ooguri, Y. Oz and Z. YinD-branes on Calabi-Yau spaces and their mirrorsNucl. Phys. B477 407 (1996), hep-th/9606112.
J. PolchinskiTASI Lectures on D-braneshep-th/9611050.
A. Polishchuk and E. ZaslowCategorical Mirror Symmetry: The Elliptic CurveAdv. Theor. Math. Phys. 2 (1998) 443–470, math.AG/9801119.
A. Recknagel and V. SchomerusD-branes in Gepner modelsNucl. Phys. B531 (1998) 185, hep-th/9712186.
M. ReidLa correspondance de McKaySé;minaire Bourbaki (novembre 1999), no. 867, math.AG/9911165.
W.-D. RuanLagrangian torus fibration and mirror symmetry of Calabi-Yau hyper-surface in toric varietymath.DG/0007028.
P. SeidelGraded Lagrangian submanifoldsmath.SG/9903049.
P. Seidel and R. P. ThomasBraid group actions on derived categories of coherent sheavesmath.AG/0001043.
A. Strominger, S.-T. Yau and E. ZaslowMirror Symmetry is T-DualityNucl.Phys. B479 (1996) 243–259, hep-th/9606040.466 M. R. Douglas
R. P. ThomasD-Branes and Mirror Symmetryto appear in the proceedings of the 2000 Clay Mathematics Institute school on Mirror Symmetry.
R. P. Thomas, to appear.
C. Voisin Mirror Symmetry, SMF/AMS Texts 1, AMS 1999.
E. WittenPhases of N=2 theories in two dimensionsNucl. Phys. B403 (1993) 159, hep-th/9301042.
E. WittenChern-Simons gauge theory as a string theoryhep-th/9207094.
E. WittenBranes and the Dynamics of QCDNucl. Phys. B507 (1997) 658; hepth/9706109.
[] I. ZharkovTorus Fibrations of Calabi-Yau Hypersurfaces in Toric Varieties and Mirror Symmetrymath.AG/9806091.
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Douglas, M.R. (2001). D-Branes on Calabi-Yau Manifolds. In: Casacuberta, C., Miró-Roig, R.M., Verdera, J., Xambó-Descamps, S. (eds) European Congress of Mathematics. Progress in Mathematics, vol 202. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8266-8_39
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DOI: https://doi.org/10.1007/978-3-0348-8266-8_39
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