sage
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a conjecture about conformal field theory
Actually, we do not know if they do since we have not seen enough examples of conformal field theory. there is a conjecture along those lines but has not been proven.
能说说这些猜想的大致内容吗?
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OK. but it is slightly more technical.
well. in 2 dimensions, the only scalar is the Ricci. thereofore, there is no ambiguity since any violation of scaling has to proportional to Ricci. However, in higher dimensions, there are other possibilities. For example, I could take two Weyl tensor and make a scalar. In principle, this could show up in conformal anomaly as well. However, it seems that (as far as I could remember) that in known examples, the term proportional to Ricci always carries the information of number of degrees of freedom of the conformal field theory. It cannot be proven this is always the case. However, it is the conjecture that this is always the case.
| 发表时间：2004-11-11, 22:54:55 |
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yinhow
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Re: a conjecture about conformal field theory
谢谢SAGE的解答.
the term proportional to Ricci always carries the information of number of degrees of freedom of the conformal field theory
number of degrees of freedom of 是指中心荷吗?
还有, 我查了一下DUFF的文章, 他是这么说的:
As showed by Polyakov, the Weyl anomaly in the worldsheet stress tensor is
given by:
\gamma^ij<T_ij>=1/24\pi(D-26)R(\gamma)
| 发表时间：2004-11-11, 23:13:08 |
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sage
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Re: a conjecture about conformal field theory
number of degrees of freedom of 是指中心荷吗?
right. Polchinski's book is very clear on this point. In bosonic string, central charge is the number of dimensions, which is the number of world sheet fields which is the number of degree of freedom
| 发表时间：2004-11-12, 01:28:07 |
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Milnor
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Re: a conjecture about conformal field theory
What do you think about the Fermi bc ghost field?
This guy has a quadratic form of central charge(depend on lambda, which is the spin).
I do not very understand the physics meaning of Fermi bc ghost field, could you explain it?
Thanks!
| 发表时间：2004-11-12, 02:11:00 |
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sage
发表文章数: 1125
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Re: a conjecture about conformal field theory
What do you think about the Fermi bc ghost field?
This guy has a quadratic form of central charge(depend on lambda, which is the spin).
I do not very understand the physics meaning of Fermi bc ghost field, could you explain it?
Thanks!
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I am not an expert on conformal field theory either.
As far as I can see, bc CFT is another example of CFT. It is useful when one BRST quantize the bosonic worldsheet CFT in string theory. In that case, it plays the role of the FP ghost in gauge theory to make the theory unitary.
the physical meaning of ghosts is that they are not physical states (since physical states would have to conserve probability and so on). however, they are useful tools in quantizing gauge theory.
| 发表时间：2004-11-12, 13:29:39 |
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Milnor
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Re: a conjecture about conformal field theory
哦，我大致理解些了，虽然在物理上不真实，但量子化时仍有用。
另外CFT是不是可以看作是共形变换下invariant的QFT,能不能作这样理解，也就是说看作一种有限制的QFT。
| 发表时间：2004-11-12, 16:40:10 |
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sage
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Re: a conjecture about conformal field theory
另外CFT是不是可以看作是共形变换下invariant的QFT,能不能作这样理解，也就是说看作一种有限制的QFT。
well. it is a special QFT in which: there is no renormalization group running of the coupling constant, there is no S-matrix, Green's functions are largely fixed by conformal symmetry....
| 发表时间：2004-11-13, 12:24:08 |
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Milnor
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Re: a conjecture about conformal field theory
largely fixed是什么意思？
| 发表时间：2004-11-13, 16:36:10 |
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卢昌海
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Re: a conjecture about conformal field theory
largely fixed 就是说很大程度上确定了。比如二维 CFT 的 2-point 及 3-point correlation function 可以被 conformal symmetry 确定到只差一个常数，4-point correlation function 可以被确定到只差一个任意函数，等。
宠辱不惊，看庭前花开花落
去留无意，望天空云卷云舒
| 发表时间：2004-11-13, 20:48:28 |
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Milnor
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Re: a conjecture about conformal field theory
I know, thx
| 发表时间：2004-11-13, 22:39:20 |
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西门吹牛
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Re: a conjecture about conformal field theory
there is no renormalization group running of the coupling constant, there is no S-matrix。
没有running of the coupling constant是跟其中的标度不变性相关吧？如何理解没有S矩阵呢？
一舞剑气动四方,天下英雄莫能挡
形踪飘忽疑无影,冷面郎君傲雪霜
| 发表时间：2004-11-14, 23:23:03 |
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sage
发表文章数: 1125
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Re: a conjecture about conformal field theory
如何理解没有S矩阵呢？
there is no way to separate particles, i.e., there is not asymptotic states which we can call one particle.
| 发表时间：2004-11-15, 11:24:04 |
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西门吹牛
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Re: a conjecture about conformal field theory
谢谢sage兄！我大致明白什么意思了，更具体的可能还要去了解数学细节。
如果标度变换是一种特殊的共形变换的话，那么conformal field theory中是否存在某种分形结构的东西呢？
一舞剑气动四方,天下英雄莫能挡
形踪飘忽疑无影,冷面郎君傲雪霜
| 发表时间：2004-11-15, 23:50:52 |
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