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【弦论】学习笔记草稿(7)中文总结

  • 2026-01-04 12:46:10
【弦论】学习笔记草稿(7)中文总结
这个笔记稍微总结一下之前学到的东西。以及鉴于我英语写得错误太多，从现在开始写中文......也方便看出来哪里写错了。
弦在target spacetime中是一维的，随时间演化扫出一个二维的世界面。相比于QFT，它的好处是一个弦图对应很多个费曼图，而且图中没有特殊的点，所以UV的行为更良好。弦的各种振动模态在低能极限下表现为不同的粒子，为不同的粒子提供了一种统一的途径。
弦的一个尺度是l_s.弦的张力=energy/(l_s^2)=energy/alpha. alpha叫
Regge slope。激发谱的质量尺度为M_s~1/l_s。
通过对D维闵氏时空下自由玻色子的弦论作用量（free boson CFT)量子化（写出运动方程，即2维波动方程，解为左行波和右行波的叠加。对左行波和右行波的系数进行量子化。），我们发现对易关系类似产生湮灭算符。但直接量子化会出现负模态或者负能量态。所以其中我们也要gauge掉2d 共形对称性。最后我们得到闭弦的谱为
注意第一行我们得到了负质量态。Phi叫做dilaton.开弦的量子化要注意由于边界条件，左行波与右行波不独立。开弦的谱为
其中，gµν对应着graviton.世界面的规范对称性直接对应着时空的规范对称性
在背景g、B下，弦的世界面作用量为
其中Phi_0项其实是Einstein-Hilbert term,是一个拓扑的项。因此世界面的作用量又可以拓扑展开，亏格为h的世界面正比于
作用量树图阶为
其中g_s=ln<Phi_0>。
另外注意要保证B-field的规范变换
意味着基本弦是带B-field的电的，也意味着基本弦不能在任意地方终止（这一点下面会讲为什么）。因为考虑B的作用量
对应的运动方程
积分得到
其中Q_1是S^{D-3}面内弦的个数，也就相当于这里B-field的电荷多少。
之前在玻色弦中我们得到了负质量态。这是不可接受的，因为会超光速。所以我们考虑了超对称弦论，它是在十维时空，有五种超弦论，我们集中讨论type II弦论。在低能下，两种type II弦论会给出有32个超荷的type II超引力。超对称弦论中没有这种负质量态，依然会有graviton, B-field, dilaton，和时空费米子。还会有一种antisymmetric的场，叫Ramond-Ramond field.弦对于它来说是中性不带电的。
type II A的RR field是奇数阶的，C_1,C_3,...,C_9(C_p代表p-form）。互相以E-M duality（电磁对偶）联系起来。type II B则是偶数阶。
T-duality指的是compactified在半径为R的圆上的弦论与半径为alpha/R的弦论等价。它提供了type II A与type IIB之间的等价关系。
由于弦论在低能极限下的有效作用量应该同样描述我们的时空，而我们时空中有RR-field，所以弦论中肯定有东西带RR电荷。考虑与p+1-form RR势能耦合的物体，世界体积是p+1维，所以
因为在平坦时空中，这种东西有无限大的体积，但张力是有限的，所以不能通过有限能量从真空中激发出来。所以不同数量的它们属于不同的superselection sector.
在弱耦合中，这种东西叫Dp-brane,是p+1维的物体。
我们上面说，规范对称性要求开弦不能在任意地方终止，实际上开弦的端点在Dp-brane上。接下来我们会说为什么。
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  134. /yingpanguazai/ssd/ssd1/www/no.67808.cn/vendor/topthink/think-view/src/Think.php ( 8.38 KB )
  135. /yingpanguazai/ssd/ssd1/www/no.67808.cn/vendor/topthink/framework/src/think/contract/TemplateHandlerInterface.php ( 1.60 KB )
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  137. /yingpanguazai/ssd/ssd1/www/no.67808.cn/vendor/topthink/think-template/src/template/driver/File.php ( 2.41 KB )
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  139. /yingpanguazai/ssd/ssd1/www/no.67808.cn/runtime/temp/6df755f970a38e704c5414acbc6e8bcd.php ( 12.06 KB )
  140. /yingpanguazai/ssd/ssd1/www/no.67808.cn/vendor/topthink/think-trace/src/Html.php ( 4.42 KB )
  1. CONNECT:[ UseTime:0.000514s ] mysql:host=127.0.0.1;port=3306;dbname=no_67808;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000674s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.005185s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.006856s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000833s ]
  6. SELECT * FROM `set` [ RunTime:0.000236s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000579s ]
  8. SELECT * FROM `article` WHERE `id` = 457930 LIMIT 1 [ RunTime:0.007694s ]
  9. UPDATE `article` SET `lasttime` = 1768290270 WHERE `id` = 457930 [ RunTime:0.011133s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.003162s ]
  11. SELECT * FROM `article` WHERE `id` < 457930 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000564s ]
  12. SELECT * FROM `article` WHERE `id` > 457930 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000621s ]
  13. SELECT * FROM `article` WHERE `id` < 457930 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.003327s ]
  14. SELECT * FROM `article` WHERE `id` < 457930 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.025471s ]
  15. SELECT * FROM `article` WHERE `id` < 457930 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.242078s ]
0.381444s