查看“︁镜像对称 (弦理论)”︁的源代码

在[[代数几何]]和[[理论物理]]中，'''镜像对称'''是指[[卡拉比-丘流形]]之间的一种特殊关系，即两种卡丘流形虽然在几何上差别很大，但是作为[[弦理论]]的[[额外维度]]时却是等价的。这样的一对流形被称为镜像流形。

镜像对称最早是由物理学家发现的。1990年左右，{{le|菲利普·坎德拉斯|Philip Candelas}}、齐妮娅·德·拉·奥萨（Xenia de la Ossa）、保罗·格林（Paul Green）和琳达·帕克斯（Linda Parks）发现它可以用于[[枚举几何]]，因此激发了数学家对此的兴趣。枚举几何是研究几何问题解的数量的数学分支。坎德拉斯和他的合作者证明了镜像对称可用于计算卡丘流形上[[有理曲线]]的数目，从而解决了一个长期的难题。尽管镜像对称最初的方法是从物理出发的，数学上并不严格，它的许多数学预测已经被[[数学证明|严格证明]]了。

目前，镜像对称是[[纯数学]]中的热门话题，数学家正在物理直觉的基础上探索镜像对称的严格数学化表述。镜像对称也是进行[[弦论]]和[[量子场论]]计算的重要工具，这两者都是物理学家用来描述[[基本粒子]]的理论。镜像对称的数学表述主要有[[马克西姆·孔采维奇]]的[[同调镜像对称]]，以及[[安德鲁·施特罗明格]]、[[丘成桐]]和{{le|埃里克·扎斯洛|Eric Zaslow}}的{{le|SYZ猜想|SYZ conjecture}}。

==参见==
* {{le|唐纳森–托马斯理论|Donaldson–Thomas theory}}
* [[Wall-crossing]]

==注释==
{{reflist|30em}}

==参考文献==
{{refbegin|30em}}
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* {{cite arXiv |last1=Hori |first1=Kentaro |last2=Vafa |first2=Cumrun |eprint=hep-th/0002222 |title=Mirror Symmetry |year=2000}}
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* {{Cite book| last1=Zaslow | first1=Eric | contribution=Mirror Symmetry | year=2008 | title=The Princeton Companion to Mathematics | url=https://archive.org/details/princetoncompani0000unse_i8p7 | editor-last=Gowers | editor-first=Timothy | isbn=978-0-691-11880-2 }}
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{{refend}}

==扩展阅读==

===科普===
* {{Cite book| first1 = Shing-Tung | last1 = Yau | first2 = Steve | last2 = Nadis | year = 2010 | title = The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions | url = https://archive.org/details/shapeofinnerspac0000yaus | publisher = Basic Books | isbn = 978-0-465-02023-2 }}
* {{cite arXiv |last=Zaslow |first=Eric |eprint=physics/0506153 |title=Physmatics |year=2005 }}
* {{Cite book| last1=Zaslow | first1=Eric | contribution=Mirror Symmetry | year=2008 | title=The Princeton Companion to Mathematics | url=https://archive.org/details/princetoncompani0000unse_i8p7 | editor-last=Gowers | editor-first=Timothy | isbn=978-0-691-11880-2 }}

===教材===
* {{cite book |editor1-first=Paul |editor1-last=Aspinwall |editor2-first=Tom |editor2-last=Bridgeland |editor3-first=Alastair |editor3-last=Craw |editor4-first=Michael |editor4-last=Douglas |editor5-first=Mark |editor5-last=Gross |editor6-first=Anton |editor6-last=Kapustin |editor7-first=Gregory |editor7-last=Moore |editor8-first=Graeme |editor8-last=Segal |editor9-first=Balázs |editor9-last=Szendröi |editor10-first=P.M.H. |editor10-last=Wilson |title=Dirichlet Branes and Mirror Symmetry |year=2009 |publisher=American Mathematical Society | isbn=978-0-8218-3848-8}}
* {{cite book |last1=Cox |first1=David |last2=Katz |first2=Sheldon |title=Mirror symmetry and algebraic geometry |url=https://archive.org/details/mirrorsymmetryal0000davi |year=1999 |publisher=American Mathematical Society |isbn=978-0-8218-2127-5}}
* {{cite book |editor1-first=Kentaro |editor1-last=Hori |editor2-first=Sheldon |editor2-last=Katz |editor3-first=Albrecht |editor3-last=Klemm |editor4-first=Rahul |editor4-last=Pandharipande |editor5-first=Richard |editor5-last=Thomas |editor6-first=Cumrun |editor6-last=Vafa |editor7-first=Ravi |editor7-last=Vakil |editor8-first=Eric |editor8-last=Zaslow |title=Mirror Symmetry |year=2003 |publisher=American Mathematical Society |url=http://math.stanford.edu/~vakil/files/mirrorfinal.pdf |isbn=0-8218-2955-6 |deadurl=yes |archiveurl=https://web.archive.org/web/20060919020706/http://math.stanford.edu/~vakil/files/mirrorfinal.pdf |archivedate=2006-09-19 }}

{{弦理论}}

[[Category:代数几何]]
[[Category:弦理论]]