Mirror symmetry (string theory) (English Wikipedia)
Analysis of information sources in references of the Wikipedia article "Mirror symmetry (string theory)" in English language version.
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ams.org
- Moore 2005, p. 214. Moore, Gregory (2005). "What is ... a Brane?" (PDF). Notices of the AMS. 52: 214. Retrieved 6 August 2016.
- Moore 2005, p. 215. Moore, Gregory (2005). "What is ... a Brane?" (PDF). Notices of the AMS. 52: 214. Retrieved 6 August 2016.
arxiv.org
- Hori & Vafa 2000. Hori, Kentaro; Vafa, Cumrun (2000). "Mirror Symmetry". arXiv:hep-th/0002222.
- Givental 1996, 1998; Lian, Liu & Yau 1997, 1999a, 1999b, 2000. Givental, Alexander (1996). "Equivariant Gromov-Witten invariants". International Mathematics Research Notices. 1996 (13): 613–663. doi:10.1155/S1073792896000414. S2CID 554844. Givental, Alexander (1998). "A mirror theorem for toric complete intersections". Topological Field Theory, Primitive Forms and Related Topics: 141–175. arXiv:alg-geom/9701016. Bibcode:1998tftp.conf..141G. doi:10.1007/978-1-4612-0705-4_5. ISBN 978-1-4612-6874-1. S2CID 2884104. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1997). "Mirror principle, I". Asian Journal of Mathematics. 1 (4): 729–763. arXiv:alg-geom/9712011. Bibcode:1997alg.geom.12011L. doi:10.4310/ajm.1997.v1.n4.a5. S2CID 8035522. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1999a). "Mirror principle, II". Asian Journal of Mathematics. 3: 109–146. arXiv:math/9905006. Bibcode:1999math......5006L. doi:10.4310/ajm.1999.v3.n1.a6. S2CID 17837291. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1999b). "Mirror principle, III". Asian Journal of Mathematics. 3 (4): 771–800. arXiv:math/9912038. Bibcode:1999math.....12038L. doi:10.4310/ajm.1999.v3.n4.a4. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (2000). "Mirror principle, IV". Surveys in Differential Geometry. 7: 475–496. arXiv:math/0007104. Bibcode:2000math......7104L. doi:10.4310/sdg.2002.v7.n1.a15. S2CID 1099024.
- Strominger, Yau & Zaslow 1996. Strominger, Andrew; Yau, Shing-Tung; Zaslow, Eric (1996). "Mirror symmetry is T-duality". Nuclear Physics B. 479 (1): 243–259. arXiv:hep-th/9606040. Bibcode:1996NuPhB.479..243S. doi:10.1016/0550-3213(96)00434-8. S2CID 14586676.
- Vafa 1992; Witten 1992. Vafa, Cumrun (1992). "Topological mirrors and quantum rings". Essays on Mirror Manifolds: 96–119. arXiv:hep-th/9111017. Bibcode:1991hep.th...11017V. ISBN 978-962-7670-01-8. Witten, Edward (1992). "Mirror manifolds and topological field theory". Essays on Mirror Manifolds: 121–160. ISBN 978-962-7670-01-8.
- Kontsevich 1995b. Kontsevich, Maxim (1995b). "Homological Algebra of Mirror Symmetry". Proceedings of the International Congress of Mathematicians. pp. 120–139. arXiv:alg-geom/9411018. Bibcode:1994alg.geom.11018K. doi:10.1007/978-3-0348-9078-6_11. ISBN 978-3-0348-9897-3. S2CID 16733945.
- Kontsevich 1995a. Kontsevich, Maxim (1995a), "Enumeration of Rational Curves Via Torus Actions", The Moduli Space of Curves, Birkhäuser, p. 335, arXiv:hep-th/9405035, doi:10.1007/978-1-4612-4264-2_12, ISBN 978-1-4612-8714-8, S2CID 16131978
- Givental 1996, 1998 Givental, Alexander (1996). "Equivariant Gromov-Witten invariants". International Mathematics Research Notices. 1996 (13): 613–663. doi:10.1155/S1073792896000414. S2CID 554844. Givental, Alexander (1998). "A mirror theorem for toric complete intersections". Topological Field Theory, Primitive Forms and Related Topics: 141–175. arXiv:alg-geom/9701016. Bibcode:1998tftp.conf..141G. doi:10.1007/978-1-4612-0705-4_5. ISBN 978-1-4612-6874-1. S2CID 2884104.
- Lian, Liu & Yau 1997, 1999a, 1999b, 2000. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1997). "Mirror principle, I". Asian Journal of Mathematics. 1 (4): 729–763. arXiv:alg-geom/9712011. Bibcode:1997alg.geom.12011L. doi:10.4310/ajm.1997.v1.n4.a5. S2CID 8035522. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1999a). "Mirror principle, II". Asian Journal of Mathematics. 3: 109–146. arXiv:math/9905006. Bibcode:1999math......5006L. doi:10.4310/ajm.1999.v3.n1.a6. S2CID 17837291. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1999b). "Mirror principle, III". Asian Journal of Mathematics. 3 (4): 771–800. arXiv:math/9912038. Bibcode:1999math.....12038L. doi:10.4310/ajm.1999.v3.n4.a4. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (2000). "Mirror principle, IV". Surveys in Differential Geometry. 7: 475–496. arXiv:math/0007104. Bibcode:2000math......7104L. doi:10.4310/sdg.2002.v7.n1.a15. S2CID 1099024.
- Intriligator & Seiberg 1996. Intriligator, Kenneth; Seiberg, Nathan (1996). "Mirror symmetry in three-dimensional gauge theories". Physics Letters B. 387 (3): 513–519. arXiv:hep-th/9607207. Bibcode:1996PhLB..387..513I. doi:10.1016/0370-2693(96)01088-X. S2CID 13985843.
doi.org
- Dixon 1988; Lerche, Vafa & Warner 1989. Dixon, Lance (1988). "Some world-sheet properties of superstring compactifications, on orbifolds and otherwise". ICTP Ser. Theoret. Phys. 4: 67–126. ISBN 978-9971-5-0452-6. Lerche, Wolfgang; Vafa, Cumrun; Warner, Nicholas (1989). "Chiral rings in superconformal theories" (PDF). Nuclear Physics B. 324 (2): 427–474. Bibcode:1989NuPhB.324..427L. doi:10.1016/0550-3213(89)90474-4. S2CID 120175708.
- Witten 1990. Witten, Edward (1990). "On the structure of the topological phase of two-dimensional gravity". Nuclear Physics B. 340 (2–3): 281–332. Bibcode:1990NuPhB.340..281W. doi:10.1016/0550-3213(90)90449-N.
- Givental 1996, 1998; Lian, Liu & Yau 1997, 1999a, 1999b, 2000. Givental, Alexander (1996). "Equivariant Gromov-Witten invariants". International Mathematics Research Notices. 1996 (13): 613–663. doi:10.1155/S1073792896000414. S2CID 554844. Givental, Alexander (1998). "A mirror theorem for toric complete intersections". Topological Field Theory, Primitive Forms and Related Topics: 141–175. arXiv:alg-geom/9701016. Bibcode:1998tftp.conf..141G. doi:10.1007/978-1-4612-0705-4_5. ISBN 978-1-4612-6874-1. S2CID 2884104. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1997). "Mirror principle, I". Asian Journal of Mathematics. 1 (4): 729–763. arXiv:alg-geom/9712011. Bibcode:1997alg.geom.12011L. doi:10.4310/ajm.1997.v1.n4.a5. S2CID 8035522. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1999a). "Mirror principle, II". Asian Journal of Mathematics. 3: 109–146. arXiv:math/9905006. Bibcode:1999math......5006L. doi:10.4310/ajm.1999.v3.n1.a6. S2CID 17837291. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1999b). "Mirror principle, III". Asian Journal of Mathematics. 3 (4): 771–800. arXiv:math/9912038. Bibcode:1999math.....12038L. doi:10.4310/ajm.1999.v3.n4.a4. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (2000). "Mirror principle, IV". Surveys in Differential Geometry. 7: 475–496. arXiv:math/0007104. Bibcode:2000math......7104L. doi:10.4310/sdg.2002.v7.n1.a15. S2CID 1099024.
- This was first observed in Kikkawa & Yamasaki 1984 and Sakai & Senda 1986. Kikkawa, Keiji; Yamasaki, Masami (1984). "Casimir effects in superstring theories". Physics Letters B. 149 (4): 357–360. Bibcode:1984PhLB..149..357K. doi:10.1016/0370-2693(84)90423-4. Sakai, Norisuke; Senda, Ikuo (1986). "Vacuum energies of string compactified on torus". Progress of Theoretical Physics. 75 (3): 692–705. Bibcode:1986PThPh..75..692S. doi:10.1143/PTP.75.692.
- Strominger, Yau & Zaslow 1996. Strominger, Andrew; Yau, Shing-Tung; Zaslow, Eric (1996). "Mirror symmetry is T-duality". Nuclear Physics B. 479 (1): 243–259. arXiv:hep-th/9606040. Bibcode:1996NuPhB.479..243S. doi:10.1016/0550-3213(96)00434-8. S2CID 14586676.
- Candelas et al. 1985. Candelas, Philip; Horowitz, Gary; Strominger, Andrew; Witten, Edward (1985). "Vacuum configurations for superstrings". Nuclear Physics B. 258: 46–74. Bibcode:1985NuPhB.258...46C. doi:10.1016/0550-3213(85)90602-9.
- This was observed in Dixon 1988 and Lerche, Vafa & Warner 1989. Dixon, Lance (1988). "Some world-sheet properties of superstring compactifications, on orbifolds and otherwise". ICTP Ser. Theoret. Phys. 4: 67–126. ISBN 978-9971-5-0452-6. Lerche, Wolfgang; Vafa, Cumrun; Warner, Nicholas (1989). "Chiral rings in superconformal theories" (PDF). Nuclear Physics B. 324 (2): 427–474. Bibcode:1989NuPhB.324..427L. doi:10.1016/0550-3213(89)90474-4. S2CID 120175708.
- Greene & Plesser 1990; Yau & Nadis 2010, p. 158. Greene, Brian; Plesser, Ronen (1990). "Duality in Calabi–Yau moduli space". Nuclear Physics B. 338 (1): 15–37. Bibcode:1990NuPhB.338...15G. doi:10.1016/0550-3213(90)90622-K. Yau, Shing-Tung; Nadis, Steve (2010). The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions. Basic Books. ISBN 978-0-465-02023-2.
- Candelas, Lynker & Schimmrigk 1990; Yau & Nadis 2010, p. 163. Candelas, Philip; Lynker, Monika; Schimmrigk, Rolf (1990). "Calabi–Yau manifolds in weighted ". Nuclear Physics B. 341 (1): 383–402. Bibcode:1990NuPhB.341..383C. doi:10.1016/0550-3213(90)90185-G. Yau, Shing-Tung; Nadis, Steve (2010). The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions. Basic Books. ISBN 978-0-465-02023-2.
- Candelas et al. 1991. Candelas, Philip; de la Ossa, Xenia; Green, Paul; Parkes, Linda (1991). "A pair of Calabi–Yau manifolds as an exactly soluble superconformal field theory". Nuclear Physics B. 359 (1): 21–74. Bibcode:1991NuPhB.359...21C. doi:10.1016/0550-3213(91)90292-6.
- Kontsevich 1995b. Kontsevich, Maxim (1995b). "Homological Algebra of Mirror Symmetry". Proceedings of the International Congress of Mathematicians. pp. 120–139. arXiv:alg-geom/9411018. Bibcode:1994alg.geom.11018K. doi:10.1007/978-3-0348-9078-6_11. ISBN 978-3-0348-9897-3. S2CID 16733945.
- Kontsevich 1995a. Kontsevich, Maxim (1995a), "Enumeration of Rational Curves Via Torus Actions", The Moduli Space of Curves, Birkhäuser, p. 335, arXiv:hep-th/9405035, doi:10.1007/978-1-4612-4264-2_12, ISBN 978-1-4612-8714-8, S2CID 16131978
- Givental 1996, 1998 Givental, Alexander (1996). "Equivariant Gromov-Witten invariants". International Mathematics Research Notices. 1996 (13): 613–663. doi:10.1155/S1073792896000414. S2CID 554844. Givental, Alexander (1998). "A mirror theorem for toric complete intersections". Topological Field Theory, Primitive Forms and Related Topics: 141–175. arXiv:alg-geom/9701016. Bibcode:1998tftp.conf..141G. doi:10.1007/978-1-4612-0705-4_5. ISBN 978-1-4612-6874-1. S2CID 2884104.
- Lian, Liu & Yau 1997, 1999a, 1999b, 2000. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1997). "Mirror principle, I". Asian Journal of Mathematics. 1 (4): 729–763. arXiv:alg-geom/9712011. Bibcode:1997alg.geom.12011L. doi:10.4310/ajm.1997.v1.n4.a5. S2CID 8035522. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1999a). "Mirror principle, II". Asian Journal of Mathematics. 3: 109–146. arXiv:math/9905006. Bibcode:1999math......5006L. doi:10.4310/ajm.1999.v3.n1.a6. S2CID 17837291. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1999b). "Mirror principle, III". Asian Journal of Mathematics. 3 (4): 771–800. arXiv:math/9912038. Bibcode:1999math.....12038L. doi:10.4310/ajm.1999.v3.n4.a4. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (2000). "Mirror principle, IV". Surveys in Differential Geometry. 7: 475–496. arXiv:math/0007104. Bibcode:2000math......7104L. doi:10.4310/sdg.2002.v7.n1.a15. S2CID 1099024.
- Intriligator & Seiberg 1996. Intriligator, Kenneth; Seiberg, Nathan (1996). "Mirror symmetry in three-dimensional gauge theories". Physics Letters B. 387 (3): 513–519. arXiv:hep-th/9607207. Bibcode:1996PhLB..387..513I. doi:10.1016/0370-2693(96)01088-X. S2CID 13985843.
harvard.edu
ui.adsabs.harvard.edu
- Dixon 1988; Lerche, Vafa & Warner 1989. Dixon, Lance (1988). "Some world-sheet properties of superstring compactifications, on orbifolds and otherwise". ICTP Ser. Theoret. Phys. 4: 67–126. ISBN 978-9971-5-0452-6. Lerche, Wolfgang; Vafa, Cumrun; Warner, Nicholas (1989). "Chiral rings in superconformal theories" (PDF). Nuclear Physics B. 324 (2): 427–474. Bibcode:1989NuPhB.324..427L. doi:10.1016/0550-3213(89)90474-4. S2CID 120175708.
- Witten 1990. Witten, Edward (1990). "On the structure of the topological phase of two-dimensional gravity". Nuclear Physics B. 340 (2–3): 281–332. Bibcode:1990NuPhB.340..281W. doi:10.1016/0550-3213(90)90449-N.
- Givental 1996, 1998; Lian, Liu & Yau 1997, 1999a, 1999b, 2000. Givental, Alexander (1996). "Equivariant Gromov-Witten invariants". International Mathematics Research Notices. 1996 (13): 613–663. doi:10.1155/S1073792896000414. S2CID 554844. Givental, Alexander (1998). "A mirror theorem for toric complete intersections". Topological Field Theory, Primitive Forms and Related Topics: 141–175. arXiv:alg-geom/9701016. Bibcode:1998tftp.conf..141G. doi:10.1007/978-1-4612-0705-4_5. ISBN 978-1-4612-6874-1. S2CID 2884104. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1997). "Mirror principle, I". Asian Journal of Mathematics. 1 (4): 729–763. arXiv:alg-geom/9712011. Bibcode:1997alg.geom.12011L. doi:10.4310/ajm.1997.v1.n4.a5. S2CID 8035522. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1999a). "Mirror principle, II". Asian Journal of Mathematics. 3: 109–146. arXiv:math/9905006. Bibcode:1999math......5006L. doi:10.4310/ajm.1999.v3.n1.a6. S2CID 17837291. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1999b). "Mirror principle, III". Asian Journal of Mathematics. 3 (4): 771–800. arXiv:math/9912038. Bibcode:1999math.....12038L. doi:10.4310/ajm.1999.v3.n4.a4. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (2000). "Mirror principle, IV". Surveys in Differential Geometry. 7: 475–496. arXiv:math/0007104. Bibcode:2000math......7104L. doi:10.4310/sdg.2002.v7.n1.a15. S2CID 1099024.
- This was first observed in Kikkawa & Yamasaki 1984 and Sakai & Senda 1986. Kikkawa, Keiji; Yamasaki, Masami (1984). "Casimir effects in superstring theories". Physics Letters B. 149 (4): 357–360. Bibcode:1984PhLB..149..357K. doi:10.1016/0370-2693(84)90423-4. Sakai, Norisuke; Senda, Ikuo (1986). "Vacuum energies of string compactified on torus". Progress of Theoretical Physics. 75 (3): 692–705. Bibcode:1986PThPh..75..692S. doi:10.1143/PTP.75.692.
- Strominger, Yau & Zaslow 1996. Strominger, Andrew; Yau, Shing-Tung; Zaslow, Eric (1996). "Mirror symmetry is T-duality". Nuclear Physics B. 479 (1): 243–259. arXiv:hep-th/9606040. Bibcode:1996NuPhB.479..243S. doi:10.1016/0550-3213(96)00434-8. S2CID 14586676.
- Candelas et al. 1985. Candelas, Philip; Horowitz, Gary; Strominger, Andrew; Witten, Edward (1985). "Vacuum configurations for superstrings". Nuclear Physics B. 258: 46–74. Bibcode:1985NuPhB.258...46C. doi:10.1016/0550-3213(85)90602-9.
- This was observed in Dixon 1988 and Lerche, Vafa & Warner 1989. Dixon, Lance (1988). "Some world-sheet properties of superstring compactifications, on orbifolds and otherwise". ICTP Ser. Theoret. Phys. 4: 67–126. ISBN 978-9971-5-0452-6. Lerche, Wolfgang; Vafa, Cumrun; Warner, Nicholas (1989). "Chiral rings in superconformal theories" (PDF). Nuclear Physics B. 324 (2): 427–474. Bibcode:1989NuPhB.324..427L. doi:10.1016/0550-3213(89)90474-4. S2CID 120175708.
- Greene & Plesser 1990; Yau & Nadis 2010, p. 158. Greene, Brian; Plesser, Ronen (1990). "Duality in Calabi–Yau moduli space". Nuclear Physics B. 338 (1): 15–37. Bibcode:1990NuPhB.338...15G. doi:10.1016/0550-3213(90)90622-K. Yau, Shing-Tung; Nadis, Steve (2010). The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions. Basic Books. ISBN 978-0-465-02023-2.
- Candelas, Lynker & Schimmrigk 1990; Yau & Nadis 2010, p. 163. Candelas, Philip; Lynker, Monika; Schimmrigk, Rolf (1990). "Calabi–Yau manifolds in weighted ". Nuclear Physics B. 341 (1): 383–402. Bibcode:1990NuPhB.341..383C. doi:10.1016/0550-3213(90)90185-G. Yau, Shing-Tung; Nadis, Steve (2010). The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions. Basic Books. ISBN 978-0-465-02023-2.
- Candelas et al. 1991. Candelas, Philip; de la Ossa, Xenia; Green, Paul; Parkes, Linda (1991). "A pair of Calabi–Yau manifolds as an exactly soluble superconformal field theory". Nuclear Physics B. 359 (1): 21–74. Bibcode:1991NuPhB.359...21C. doi:10.1016/0550-3213(91)90292-6.
- Vafa 1992; Witten 1992. Vafa, Cumrun (1992). "Topological mirrors and quantum rings". Essays on Mirror Manifolds: 96–119. arXiv:hep-th/9111017. Bibcode:1991hep.th...11017V. ISBN 978-962-7670-01-8. Witten, Edward (1992). "Mirror manifolds and topological field theory". Essays on Mirror Manifolds: 121–160. ISBN 978-962-7670-01-8.
- Kontsevich 1995b. Kontsevich, Maxim (1995b). "Homological Algebra of Mirror Symmetry". Proceedings of the International Congress of Mathematicians. pp. 120–139. arXiv:alg-geom/9411018. Bibcode:1994alg.geom.11018K. doi:10.1007/978-3-0348-9078-6_11. ISBN 978-3-0348-9897-3. S2CID 16733945.
- Givental 1996, 1998 Givental, Alexander (1996). "Equivariant Gromov-Witten invariants". International Mathematics Research Notices. 1996 (13): 613–663. doi:10.1155/S1073792896000414. S2CID 554844. Givental, Alexander (1998). "A mirror theorem for toric complete intersections". Topological Field Theory, Primitive Forms and Related Topics: 141–175. arXiv:alg-geom/9701016. Bibcode:1998tftp.conf..141G. doi:10.1007/978-1-4612-0705-4_5. ISBN 978-1-4612-6874-1. S2CID 2884104.
- Lian, Liu & Yau 1997, 1999a, 1999b, 2000. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1997). "Mirror principle, I". Asian Journal of Mathematics. 1 (4): 729–763. arXiv:alg-geom/9712011. Bibcode:1997alg.geom.12011L. doi:10.4310/ajm.1997.v1.n4.a5. S2CID 8035522. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1999a). "Mirror principle, II". Asian Journal of Mathematics. 3: 109–146. arXiv:math/9905006. Bibcode:1999math......5006L. doi:10.4310/ajm.1999.v3.n1.a6. S2CID 17837291. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1999b). "Mirror principle, III". Asian Journal of Mathematics. 3 (4): 771–800. arXiv:math/9912038. Bibcode:1999math.....12038L. doi:10.4310/ajm.1999.v3.n4.a4. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (2000). "Mirror principle, IV". Surveys in Differential Geometry. 7: 475–496. arXiv:math/0007104. Bibcode:2000math......7104L. doi:10.4310/sdg.2002.v7.n1.a15. S2CID 1099024.
- Intriligator & Seiberg 1996. Intriligator, Kenneth; Seiberg, Nathan (1996). "Mirror symmetry in three-dimensional gauge theories". Physics Letters B. 387 (3): 513–519. arXiv:hep-th/9607207. Bibcode:1996PhLB..387..513I. doi:10.1016/0370-2693(96)01088-X. S2CID 13985843.
dash.harvard.edu
- Dixon 1988; Lerche, Vafa & Warner 1989. Dixon, Lance (1988). "Some world-sheet properties of superstring compactifications, on orbifolds and otherwise". ICTP Ser. Theoret. Phys. 4: 67–126. ISBN 978-9971-5-0452-6. Lerche, Wolfgang; Vafa, Cumrun; Warner, Nicholas (1989). "Chiral rings in superconformal theories" (PDF). Nuclear Physics B. 324 (2): 427–474. Bibcode:1989NuPhB.324..427L. doi:10.1016/0550-3213(89)90474-4. S2CID 120175708.
- This was observed in Dixon 1988 and Lerche, Vafa & Warner 1989. Dixon, Lance (1988). "Some world-sheet properties of superstring compactifications, on orbifolds and otherwise". ICTP Ser. Theoret. Phys. 4: 67–126. ISBN 978-9971-5-0452-6. Lerche, Wolfgang; Vafa, Cumrun; Warner, Nicholas (1989). "Chiral rings in superconformal theories" (PDF). Nuclear Physics B. 324 (2): 427–474. Bibcode:1989NuPhB.324..427L. doi:10.1016/0550-3213(89)90474-4. S2CID 120175708.
semanticscholar.org
api.semanticscholar.org
- Dixon 1988; Lerche, Vafa & Warner 1989. Dixon, Lance (1988). "Some world-sheet properties of superstring compactifications, on orbifolds and otherwise". ICTP Ser. Theoret. Phys. 4: 67–126. ISBN 978-9971-5-0452-6. Lerche, Wolfgang; Vafa, Cumrun; Warner, Nicholas (1989). "Chiral rings in superconformal theories" (PDF). Nuclear Physics B. 324 (2): 427–474. Bibcode:1989NuPhB.324..427L. doi:10.1016/0550-3213(89)90474-4. S2CID 120175708.
- Givental 1996, 1998; Lian, Liu & Yau 1997, 1999a, 1999b, 2000. Givental, Alexander (1996). "Equivariant Gromov-Witten invariants". International Mathematics Research Notices. 1996 (13): 613–663. doi:10.1155/S1073792896000414. S2CID 554844. Givental, Alexander (1998). "A mirror theorem for toric complete intersections". Topological Field Theory, Primitive Forms and Related Topics: 141–175. arXiv:alg-geom/9701016. Bibcode:1998tftp.conf..141G. doi:10.1007/978-1-4612-0705-4_5. ISBN 978-1-4612-6874-1. S2CID 2884104. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1997). "Mirror principle, I". Asian Journal of Mathematics. 1 (4): 729–763. arXiv:alg-geom/9712011. Bibcode:1997alg.geom.12011L. doi:10.4310/ajm.1997.v1.n4.a5. S2CID 8035522. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1999a). "Mirror principle, II". Asian Journal of Mathematics. 3: 109–146. arXiv:math/9905006. Bibcode:1999math......5006L. doi:10.4310/ajm.1999.v3.n1.a6. S2CID 17837291. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (1999b). "Mirror principle, III". Asian Journal of Mathematics. 3 (4): 771–800. arXiv:math/9912038. Bibcode:1999math.....12038L. doi:10.4310/ajm.1999.v3.n4.a4. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung (2000). "Mirror principle, IV". Surveys in Differential Geometry. 7: 475–496. arXiv:math/0007104. Bibcode:2000math......7104L. doi:10.4310/sdg.2002.v7.n1.a15. S2CID 1099024.
- Strominger, Yau & Zaslow 1996. Strominger, Andrew; Yau, Shing-Tung; Zaslow, Eric (1996). "Mirror symmetry is T-duality". Nuclear Physics B. 479 (1): 243–259. arXiv:hep-th/9606040. Bibcode:1996NuPhB.479..243S. doi:10.1016/0550-3213(96)00434-8. S2CID 14586676.
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