메뉴 건너뛰기




Volumn 59, Issue 5, 2004, Pages 907-940

Lectures on mirror symmetry, derived categories, and D-branes

Author keywords

[No Author keywords available]

Indexed keywords


EID: 14544308714     PISSN: 00360279     EISSN: 14684829     Source Type: Journal    
DOI: 10.1070/RM2004v059n05ABEH000772     Document Type: Article
Times cited : (21)

References (53)
  • 1
    • 33745054164 scopus 로고    scopus 로고
    • Derived categories and zero-brane stability
    • paper 4.
    • P. S. Aspinwall and A. E. Lawrence, "Derived categories and zero-brane stability", J. High Energy Phys. 2001, no 8, paper 4.
    • (2001) J. High Energy Phys. , vol.8
    • Aspinwall, P.S.1    Lawrence, A.E.2
  • 3
    • 0009596208 scopus 로고
    • Framed triangulated categories
    • A. I. Bondal and M. M. Kapranov, "Framed triangulated categories", Mat. Sb. 181 (1990), 669-683; English transl., Math. USSR-Sb. 70 (1991), 93-107.
    • (1990) Mat. Sb. , vol.181 , pp. 669-683
    • Bondal, A.I.1    Kapranov, M.M.2
  • 4
    • 14544299166 scopus 로고
    • English transl.
    • A. I. Bondal and M. M. Kapranov, "Framed triangulated categories", Mat. Sb. 181 (1990), 669-683; English transl., Math. USSR-Sb. 70 (1991), 93-107.
    • (1991) Math. USSR-Sb. , vol.70 , pp. 93-107
  • 6
    • 33744506688 scopus 로고    scopus 로고
    • Enhanced D-brane categories from string field theory
    • paper 16
    • D.-E. Diaconescu, "Enhanced D-brane categories from string field theory", J. High Energy Phys. 2001, no. 6, paper 16.
    • (2001) J. High Energy Phys. , vol.6
    • Diaconescu, D.-E.1
  • 7
    • 0003310196 scopus 로고
    • Intersection theory, integrable hierarchies and topological field theory
    • New Symmetry Principles in Quantum Field Theory (Cargèse, 1991), Plenum, New York
    • R. Dijkgraaf, "Intersection theory, integrable hierarchies and topological field theory", New Symmetry Principles in Quantum Field Theory (Cargèse, 1991), (NATO Adv. Sci. Inst. Ser. B Phys., vol. 295) Plenum, New York 1992, pp. 95-158.
    • (1992) NATO Adv. Sci. Inst. Ser. B Phys. , vol.295 , pp. 95-158
    • Dijkgraaf, R.1
  • 8
    • 0035402802 scopus 로고    scopus 로고
    • D-branes, categories and N = 1 supersymmetry
    • M. R. Douglas, "D-branes, categories and N = 1 supersymmetry", J. Math. Phys. 42 (2001), 2818-2843.
    • (2001) J. Math. Phys. , vol.42 , pp. 2818-2843
    • Douglas, M.R.1
  • 11
    • 0041844281 scopus 로고    scopus 로고
    • Lectures on conformal field theory
    • (Princeton, NJ, 1996/1997), Amer. Math. Soc., Providence, RI
    • K. Gawȩdzki, "Lectures on conformal field theory", Quantum Fields and Strings: A Course for Mathematicians, vols. I, II (Princeton, NJ, 1996/1997), Amer. Math. Soc., Providence, RI 1999, pp. 727-805.
    • (1999) Quantum Fields and Strings: A Course for Mathematicians , vol.1-2 , pp. 727-805
    • Gawȩdzki, K.1
  • 12
    • 33745701144 scopus 로고
    • The Schouten bracket and Hamiltonian operators
    • I. M. Gel'fand and I. Ya. Dorfman, "The Schouten bracket and Hamiltonian operators", Funktsional. Anal. i Prilozhen. 14:3 (1980), 71-74; English transl., Funct. Anal. Appl. 14 (1981), 223-226.
    • (1980) Funktsional. Anal. i Prilozhen. , vol.14 , Issue.3 , pp. 71-74
    • Gel'fand, I.M.1    Dorfman, I.Ya.2
  • 13
    • 85164648594 scopus 로고
    • English transl.
    • I. M. Gel'fand and I. Ya. Dorfman, "The Schouten bracket and Hamiltonian operators", Funktsional. Anal. i Prilozhen. 14:3 (1980), 71-74; English transl., Funct. Anal. Appl. 14 (1981), 223-226.
    • (1981) Funct. Anal. Appl. , vol.14 , pp. 223-226
  • 15
    • 85164646377 scopus 로고
    • English transl.
    • S. I. Gel'fand and Yu. I. Manin, Methods of homological algebras, vol. I, Nauka, Moscow 1988; English transl., Encyclopaedia Math. Sci., vol. 38 1994, pp. 1-222.
    • (1994) Encyclopaedia Math. Sci. , vol.38 , pp. 1-222
  • 16
    • 0035615031 scopus 로고    scopus 로고
    • Mirror symmetry for abelian varieties
    • V. Golyshev, V. Lunts, and D. Orlov, "Mirror symmetry for abelian varieties", J. Algebraic Geom. 10 (2001), 433-496.
    • (2001) J. Algebraic Geom. , vol.10 , pp. 433-496
    • Golyshev, V.1    Lunts, V.2    Orlov, D.3
  • 17
    • 0002493947 scopus 로고
    • Duality in Calabi-Yau moduli space
    • B. R. Greene and M. R. Plesser, "Duality in Calabi-Yau moduli space", Nuclear Phys. B 338 (1990), 15-37.
    • (1990) Nuclear Phys. B , vol.338 , pp. 15-37
    • Greene, B.R.1    Plesser, M.R.2
  • 18
    • 0003863845 scopus 로고
    • (Lecture Notes in Math.) Springer-Verlag, Berlin
    • R. Hartshorne, Residues and duality, (Lecture Notes in Math., vol. 20) Springer-Verlag, Berlin 1966.
    • (1966) Residues and Duality , vol.20
    • Hartshorne, R.1
  • 21
    • 13244294486 scopus 로고    scopus 로고
    • Topological strings on noncommutative manifolds
    • A. Kapustin, "Topological strings on noncommutative manifolds", Int. J. Geom. Methods Mod. Phys. 1:1-2 (2004), 49-81.
    • (2004) Int. J. Geom. Methods Mod. Phys. , vol.1 , Issue.1-2 , pp. 49-81
    • Kapustin, A.1
  • 22
    • 0037324076 scopus 로고    scopus 로고
    • Vertex algebras, mirror symmetry, and D-branes: The case of complex tori
    • A. Kapustin and D. Orlov, "Vertex algebras, mirror symmetry, and D-branes: The case of complex tori", Comm. Math. Phys. 233 (2003), 79-136.
    • (2003) Comm. Math. Phys. , vol.233 , pp. 79-136
    • Kapustin, A.1    Orlov, D.2
  • 23
    • 0041426659 scopus 로고    scopus 로고
    • Remarks on A-branes, mirror symmetry, and the Fukaya category
    • A. Kapustin and D. Orlov, "Remarks on A-branes, mirror symmetry, and the Fukaya category", J. Geom. Phys. 48:1 (2003), 84-99.
    • (2003) J. Geom. Phys. , vol.48 , Issue.1 , pp. 84-99
    • Kapustin, A.1    Orlov, D.2
  • 24
  • 25
    • 85164641822 scopus 로고
    • English transl. Springer-Verlag, Berlin-Heidelberg
    • M. Kashiwara and P. Shapira, Sheaves on manifolds, Mir, Moscow 1997; English transl., (Grundlehren 292) Springer-Verlag, Berlin-Heidelberg 1990.
    • (1990) Grundlehren , vol.292
  • 26
    • 79551513620 scopus 로고    scopus 로고
    • D-branes, open string vertex operators, and Ext groups
    • S. Katz and E. Sharpe, "D-branes, open string vertex operators, and Ext groups", Adv. Theor. Math. Phys. 6 (2002), 979-1030.
    • (2002) Adv. Theor. Math. Phys. , vol.6 , pp. 979-1030
    • Katz, S.1    Sharpe, E.2
  • 27
    • 70350091140 scopus 로고    scopus 로고
    • Derived categories and their uses
    • (M. Hazewinkel, ed.), North-Holland, Amsterdam
    • B. Keller, "Derived categories and their uses", Handbook of Algebra, vol. I (M. Hazewinkel, ed.), North-Holland, Amsterdam 1996, pp. 671-701.
    • (1996) Handbook of Algebra , vol.1 , pp. 671-701
    • Keller, B.1
  • 28
    • 0007370748 scopus 로고    scopus 로고
    • ∞-infinity algebras and modules
    • ∞-infinity algebras and modules", Homology Homotopy Appl. 3:1 (2001), 1-35.
    • (2001) Homology Homotopy Appl. , vol.3 , Issue.1 , pp. 1-35
    • Keller, B.1
  • 31
    • 0035844777 scopus 로고    scopus 로고
    • On the structure of open-closed topological field theory in two dimensions
    • C. I. Lazaroiu, "On the structure of open-closed topological field theory in two dimensions", Nuclear Phys. B 603 (2001), 497-530.
    • (2001) Nuclear Phys. B , vol.603 , pp. 497-530
    • Lazaroiu, C.I.1
  • 32
    • 33744759596 scopus 로고    scopus 로고
    • Unitarity, D-brane dynamics and D-brane categories
    • paper 31
    • C. I. Lazaroiu, "Unitarity, D-brane dynamics and D-brane categories", J. High Energy Phys. 2001, no. 12, paper 31.
    • (2001) J. High Energy Phys. , vol.12
    • Lazaroiu, C.I.1
  • 33
    • 33646049827 scopus 로고
    • Chiral rings in N = 2 superconformal theories
    • W. Lerche, C. Vafa, and N. P. Warner, "Chiral rings in N = 2 superconformal theories", Nuclear Phys. B 324 (1989), 427-474.
    • (1989) Nuclear Phys. B , vol.324 , pp. 427-474
    • Lerche, W.1    Vafa, C.2    Warner, N.P.3
  • 35
    • 85164634774 scopus 로고    scopus 로고
    • D-branes, RR-fields and K-theory
    • G. Moore, "D-branes, RR-fields and K-theory", The Duality Workshop (2001), http://online.itp.ucsb.edu/online/mp01.
    • (2001) The Duality Workshop , pp. 01
    • Moore, G.1
  • 36
    • 84972539524 scopus 로고
    • Duality between D(X) and D(X̂) with its application to Picard sheaves
    • S. Mukai, "Duality between D(X) and D(X̂) with its application to Picard sheaves", Nagoya Math. J. 81 (1981), 153-175.
    • (1981) Nagoya Math. J. , vol.81 , pp. 153-175
    • Mukai, S.1
  • 37
    • 0000439288 scopus 로고    scopus 로고
    • Equivalences of derived categories and K3 surfaces
    • D. O. Orlov, "Equivalences of derived categories and K3 surfaces", J. Math. Sci. (New York) 84 (1997), 1361-1381.
    • (1997) J. Math. Sci. (New York) , vol.84 , pp. 1361-1381
    • Orlov, D.O.1
  • 38
    • 0242380986 scopus 로고    scopus 로고
    • Derived categories of coherent sheaves on abelian varieties and equivalences between themIzv
    • D. O. Orlov, "Derived categories of coherent sheaves on abelian varieties and equivalences between them", Izv. Ross. Akad. Nauk Ser. Mat. 66:3 (2002), 131-158; English transl., Izv. Math. 66 (2002), 569-594.
    • (2002) Ross. Akad. Nauk Ser. Mat. , vol.66 , Issue.3 , pp. 131-158
    • Orlov, D.O.1
  • 39
    • 0242380986 scopus 로고    scopus 로고
    • English transl.
    • D. O. Orlov, "Derived categories of coherent sheaves on abelian varieties and equivalences between them", Izv. Ross. Akad. Nauk Ser. Mat. 66:3 (2002), 131-158; English transl., Izv. Math. 66 (2002), 569-594.
    • (2002) Izv. Math. , vol.66 , pp. 569-594
  • 40
    • 0242382578 scopus 로고    scopus 로고
    • Derived categories of coherent sheaves and equivalences between them
    • D. O. Orlov, "Derived categories of coherent sheaves and equivalences between them", Uspekhi Mat. Nauk 58:3 (2003), 89-172; English transl., Russian Math. Surveys 58 (2003), 511-591.
    • (2003) Uspekhi Mat. Nauk , vol.58 , Issue.3 , pp. 89-172
    • Orlov, D.O.1
  • 41
    • 0242382578 scopus 로고    scopus 로고
    • English transl.
    • D. O. Orlov, "Derived categories of coherent sheaves and equivalences between them", Uspekhi Mat. Nauk 58:3 (2003), 89-172; English transl., Russian Math. Surveys 58 (2003), 511-591.
    • (2003) Russian Math. Surveys , vol.58 , pp. 511-591
  • 42
    • 0003407720 scopus 로고    scopus 로고
    • String theory, Cambridge University Press, Cambridge
    • J. Polchinski, String theory, vol. II: Superstring theory and beyond, Cambridge University Press, Cambridge 1998.
    • (1998) Superstring Theory and beyond , vol.2
    • Polchinski, J.1
  • 43
    • 8644257680 scopus 로고
    • Dirichlet-branes and Ramond-Ramond charges
    • J. Polchinski, "Dirichlet-branes and Ramond-Ramond charges", Phys. Rev. Lett. 75 (1995), 4724-4727.
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 4724-4727
    • Polchinski, J.1
  • 44
    • 0030300392 scopus 로고    scopus 로고
    • Symplectic biextensions and generalization of the Fourier-Mukai transforms
    • A. Polishchuk, "Symplectic biextensions and generalization of the Fourier-Mukai transforms", Math. Res. Lett. 3 (1996), 813-828.
    • (1996) Math. Res. Lett. , vol.3 , pp. 813-828
    • Polishchuk, A.1
  • 45
    • 0001623086 scopus 로고    scopus 로고
    • Categorical mirror symmetry: The elliptic curve
    • A. Polishchuk and E. Zaslow, "Categorical mirror symmetry: The elliptic curve", Adv. Theor. Math. Phys. 2 (1998), 443-470.
    • (1998) Adv. Theor. Math. Phys. , vol.2 , pp. 443-470
    • Polishchuk, A.1    Zaslow, E.2
  • 46
    • 0003910255 scopus 로고
    • The definition of conformal field theory
    • Differential Geometrical Methods in Theoretical Physics (Como, 1987) Kluwer, Dordrecht
    • G. B. Segal, "The definition of conformal field theory", Differential Geometrical Methods in Theoretical Physics (Como, 1987), (NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 250) Kluwer, Dordrecht 1988, pp. 165-171.
    • (1988) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. , vol.250 , pp. 165-171
    • Segal, G.B.1
  • 48
    • 0030575209 scopus 로고    scopus 로고
    • Hochschild cohomology of quasiprojective schemes
    • R. G. Swan, "Hochschild cohomology of quasiprojective schemes", J. Pure Appl. Algebra 110:1 (1996), 57-80.
    • (1996) J. Pure Appl. Algebra , vol.110 , Issue.1 , pp. 57-80
    • Swan, R.G.1
  • 49
    • 0000429325 scopus 로고
    • Catégories dérivées
    • Cohomologie Étale. Séminaire de Géométrie Algébrique du Bois-Marie SGA 4 1/2 Springer-Verlag, Berlin
    • J. L. Verdier, "Catégories dérivées", Cohomologie Étale. Séminaire de Géométrie Algébrique du Bois-Marie SGA 4 1/2, (Lecture Notes in Math., vol. 569.) Springer-Verlag, Berlin 1977, pp. 262-311.
    • (1977) Lecture Notes in Math. , vol.569 , pp. 262-311
    • Verdier, J.L.1
  • 50
    • 0010022959 scopus 로고
    • Phases of N = 2 theories in two dimensions
    • E. Witten, "Phases of N = 2 theories in two dimensions", Nucl. Phys. B 403 (1993), 159-222.
    • (1993) Nucl. Phys. B , vol.403 , pp. 159-222
    • Witten, E.1
  • 51
    • 1542511960 scopus 로고
    • Topological sigma models
    • E. Witten, "Topological sigma models", Comm. Math. Phys. 118 (1988), 411-449.
    • (1988) Comm. Math. Phys. , vol.118 , pp. 411-449
    • Witten, E.1
  • 52
    • 0004339142 scopus 로고
    • Mirror manifolds and topological field theory
    • Internat. Press, Hong Kong
    • E. Witten, "Mirror manifolds and topological field theory", Essays on Mirror Manifolds, Internat. Press, Hong Kong 1992, pp. 120-158.
    • (1992) Essays on Mirror Manifolds , pp. 120-158
    • Witten, E.1
  • 53
    • 0001753344 scopus 로고
    • Chern-Simons gauge theory as a string theory
    • The Floer Memorial Volume Birkhaüser, Basel
    • E. Witten, "Chern-Simons gauge theory as a string theory", The Floer Memorial Volume, (Progr. Math., vol. 133) Birkhaüser, Basel 1995, pp. 637-678.
    • (1995) Progr. Math. , vol.133 , pp. 637-678
    • Witten, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.