Timeline for Why Weyl invariance is important for consistent string theory?
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| Apr 13, 2017 at 12:39 | history | edited | CommunityBot |
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| Aug 3, 2016 at 8:04 | history | edited | Qmechanic♦ | CC BY-SA 3.0 |
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| Aug 17, 2013 at 16:14 | history | edited | user26143 | CC BY-SA 3.0 |
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| Aug 17, 2013 at 3:05 | history | tweeted | twitter.com/#!/StackPhysics/status/368569231232602112 | ||
| Aug 17, 2013 at 2:16 | answer | added | user10001 | timeline score: 12 | |
| Aug 16, 2013 at 23:21 | comment | added | user26143 | Sorry, how to see the cancellation of unphysical degree of freedom using the invariances. Would you suggest any reference? Thank you very much! | |
| Aug 16, 2013 at 22:37 | history | edited | user26143 | CC BY-SA 3.0 |
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| Aug 16, 2013 at 22:01 | comment | added | user10001 | i too don't understand Polchinski's argument;) May be he wants to say that since the counterterm for the divergence is non Weyl invariant so the divergence itself has to do with non-Weyl invariance and so it should not be there. But whether or not the divergence has anything to do with non-Weyl invariance it should anyway be regularized ! However in any case the idea is that Weyl invariance is necessary to get rid of unphysical metric degrees of freedom and so one demands that the Weyl invariance remain preserved under quantization. May be I will write an answer after understanding it properly | |
| Aug 16, 2013 at 20:07 | comment | added | user26143 | Sorry I don't get it. Maybe I can start from a different question, in p22 of Polchinski's book, there is a divergence term in the zero point energy of open-string (1.3.34), $$ \frac{D-2}{2} \frac{ 2l p^+ \alpha'}{ \epsilon^2 \pi } $$. It is said "In fact, Weyl invariance requires that it be cancelled" Why? How it works? | |
| Aug 16, 2013 at 17:22 | comment | added | user10001 | In case of string theory the three components of worldsheet metric tensor are unphysical degrees of freedom. Reparametrization invariance along the two directions on a worldsheet can cancel 2 of them. To cancel the third one you need Weyl invarince. If you don't care about preserving Weyl symmetry then one of three degrees of freedom of the metric will not be canceled. This left out degree of freedom is i think called Liouville mode and corresponding string theories are known as noncritical string theories | |
| Aug 16, 2013 at 16:46 | history | asked | user26143 | CC BY-SA 3.0 |